**You can read about my work in the article ****118*** .
For lectures and Conference talks, click
here*.

__Publications__

**Clicking the number will give you the paper(if available) in
dvi or ps or pdf format: **

**Book (with R. Tijdeman) Exponential Diophantine equations,
Cambridge Tracts in Mathematics 87 (1986), Cambridge University P**

**132 (with Clemens Fuchs) ****Divisibility
properties of hypergeometric polynomials, ****submitted.**

**131 (with F. Luca)
****Products of Fibonacci numbers with indices in an interval
and at most four omitted being a power, ****submitted.**

**130 (with S. Laishram) ****Irreducibility
of generalized Hermite-Laguerre Polynomials II,Indag****.
Math., 20 (2009), 427-434.**

**129 (with S. Laishram) ****Extensions
of Schur's irreducibility results, ****submitted.**

**128 (with S. Laishram)
****Irreducibility of generalized Hermite-Laguerre Polynomials,
****submitted.**

**127 (with N. Saradha) ****Almost
perfect powers in consecutive integers (II), ****Indag.
Math., N.S. 19 (2009), 649-658.**

**126 (with Clemens Fuchs) ****Divisibility
properties of generalized Laguerre polynomials, ****Indag.
Math., ****Indag****.
Math., 20 (2009), 217-231.**

**125 (with Rob Tijdeman)
****Generalisations of some irreducibility results of Schur,
****Acta Arith., to appear.**

**124 (with R Balasubramanian, Shanta
Laishram and R Thangadurai) ****The number of prime divisors of
consecutive integers, ****Jour.
of Combinatorics and Number Theory, 1 (2009), 65-73.**

**123 (with Shanta Laishram, Szabolcs
Tengely ) ****Squares in products in arithmetic progression
with at most one term omitted and common difference a prime power,
****Acta Arith. 135 (2008),
143-158.**

**122 (with Florian Luca )
****Products of members of Lucas sequences with indices in an
interval being a power, ****Journal of Number Theory, 129
(2009),303-315. **

**121** **Theorems of Sylvester
and Schur****, Math. Student (2008).**

**120 (with Florian Luca)
****Diophantine equations with products of consecutive terms in
Lucas sequences II, ****Acta
Arith. 133 (2008), 53-71.**

**119 Some
****topics in Prime number theory****,
Mathematics Newsletter, Ramanujan Mathematical Society 18 (2008),
62-67.**

**118 ****Diophantine
approximations, Diophantine equations, Transcendence and
Applications, ****Indian Jour. of Pure and Applied Math, 37
(2006), 9-39. **

**117 (with Shanta
Laishram) ****Squares in products in arithmetic progression
with at most two terms omitted and common difference a prime power,
****Acta Arith., 134(2008),
299-316. **

**116 (with Shanta
Laishram) ****The equation {\bf $n(n+d) \cdots (n+(k-1)d) =
b y^2$} with $\omega(d)\le 6$ or $d\le 10^{10}$,**** Acta
Arith., 129 (2007), 249-305.**

**115 (with Noriko Hirata-Kohno,
Shanta Laishram, R.
Tijdeman) ****An Extension of a Theorem of Euler,****
Acta Arith., 129 (2007), 71-102.**

**114 (with R. Tijdeman) ****Prime
factors of arithmetic progressions and binomial coefficients,
****Diophantine****
****Geomtry****,
****edited by Umberto
Zannier, Edizioni Della Normale, Pisa (2007), 283-296.**** **

**113 (with N. Saradha) ****On
the equation n(n+d) ... (n+(i-1)d)(n+(i+1)d) ... (n+(k-1)d) = y^l
with 0 < i< k-1 ****, Acta Arith., 129 (2007), 1-21.**

**112 (with Shanta
Laishram ) ****Grimm's Conjecture on consecutive integers,
****International Journal of Number Theory, 2 (2006), 1-5.**

**111 (with Shanta
Laishram ) ****The greatest prime divisor of a product of
terms in an arithmetic progression, ****Indag. Math, 17(2006),
425-436.**

**110 ****Powers in arithmetic
progress (III) ****, The Riemann Zeta function and related
themes, Ramanujan Math. Society Publication, (2006), 131-140. **

**109 (with Shanta
Laishram ) ****The greatest prime divisor of a product of
consecutive integers, ****Acta Arith., 120 (2005), 299-306.**

**108 (with F. Luca) ****Diophantine
equations with products of consecutive terms in Lucas sequences****,
Journal of Number Theory, 114 (2005), 541-560. **

**107 (with N. Saradha)
****Contributions towards a conjecture of Erdos on
perfect powers in arithmetic progressions****, Compositio
Math., 141 (2005), 541-560. **

**106 (with Shanta
Laishram ) ****Number of prime divisors in a
product of terms of an arithmetic progression****, Indag.
Math., 15 (2004), 505-521. **

**105 (Anirban Mukhopadhyay) ****Almost
squares in arithmetic progression (III)****, Indag.
Math., 15 (2004), 523-533. **

**104 (with Shanta
Laishram ) ****Number of prime divisors in a
product of consecutive integers****, Acta Arith. 113 (2004),
327-341. **

**103 ****Approximations of
algebraic numbers by rationals: A theorem of Thue****,
Elliptic Curves, Modular Forms and Cryptography ed. By A.K. Bhandari,
**

**D.S. Nagraj, B. Ramakrishnan, T.N. Venkataramana, Hinustan Book
Agency ( 2003 ), 119-137.**

**102 ****The generalised
Ramanujan-Nagell equation****, Applicable Mathematics in
the Golden Age, edited by J.C. Mishra, Narosa (2003), 490-495. **

**101 (with Anirban Mukhopadhyay) ****Square
free part of products of consecutive integers****, Publ.
Math. Debrecen, 64 (2004), 79-99. **

**100 (Anirban Mukhopadhyay)
****Almost squares in arithmetic progression (II)****,
Acta Arith., (2003), 1-14. **

**99 (with Y. Bugeaud) ****On
an equation of Goomaghtigh II****, Pacific Jour. Math. 207
(2002), 61-76. **

**98 (with N. Saradha) ****Almost
squares and factorisations in consecutive integers****,
Compositio Math. 138 (2003), 113-124. **

**97 (with N. Saradha)
****Almost squares in arithmetic progression****,
Compositio Math., 138 (2003), 73-111. **

**96 ****Powers in
arithmetic progression (II)****, Analytic Number Theory, RIMS
Kokyuroku (2002), Kyoto University, to appear. **

**95 ****Powers in
arithmetic progression****, A Panorama in Number Theory or The
View from Baker's Garden, edited by G.Wustholz, Cambridge University
Press (2002), 341-353. **

**94 ****An equation of
Goormaghtigh and diophantine approximations****, Current
Trends in Number Theory, edited by S.D.Adhikari, S.A.Katre and
B.Ramakrishnan, Hindustan Book Agency, New Delhi (2002), 185-197. **

**93 (with N. Saradha
and R. Tijdeman) ****Some extensions and refinements of a
theorem of Sylvester****, Acta Arith. 102 (2002), 167-181. **

**92 (with Y. Bugeaud), ****On
the number of solutions of the generalised Ramanujan-Nagell equation****,
Jour. Reine Angew. Math. 539 (2001), 55-74. **

**91 ****Mathematical
Contributions****, Bulletin Bombay Mathematical Colloquium 15
(1999) published in 2001, 1-19. **

**90 (with S. D. Adhikari, N.
Saradha and R. Tijdeman) ****Transcendental Infinite Sums****,
Indag. Math. N.S. 12 (2001), 1-14. **

**89 (with G. Hanrot and N.
Saradha) ****Almost perfect powers in consecutive integers****,
Acta Arith. 99 (2001), 13-25. **

**88 (with N. Saradha) ****Almost
perfect powers in arithmetic progression****, Acta Arith. 99
(2001), 363-388. **

**87 ****Some conjectures
in the theory of exponential diophantine equations****,
Publicationes Math. Debrecen 56 (2000), 631-641. **

**86 (with Y. Bugeaud, M. Mignotte
and Y. Roy) ****The equation $\frac{x^n-1}{x-1} = y^q$ has no
solution with $x$ square****, Math. Proc. Camb. Phil. Soc. 127
(1999), 353-372. **

**85 (with N. Saradha) ****The
equation $\frac{x^n-1}{x-1} = y^q$ with $x$ square****, Math.
Proc. Camb. Phil. Soc. 125 (1999), 1-19. **

**84 (with F. Beukers and R. Tijdeman)
****Irreducibility of polynomials and arithmetic progressions
with equal products of terms****, Number Theory in Progress,
Volume 1 (1999), Walter de Gruyter, Berlin, 11-26. **

**83 ****The equation
$a\frac{x^n-1}{x-1} = by^q$ with $ab > 1$****, Number
Theory in Progress, Volume 1 (1999), Walter de Gruyter, Berlin,
473-485. **

**82 ****Exponential
diophantine equations involving products of consecutive integers and
related equations****, Number Theory edited by R.P.Bambah,
V.C.Dumir and R.J.Hans-Gill, Hindustan Book Agency (1999), 463-495. **

**81 (with Yu.V. Nesterenko) ****On
an equation of Goormaghtigh****, Acta Arith. 83 (1998),
381-389. **

**80 Integer solutions of exponential diophantine
equations, Bulletin of Bombay Mathematical Colloquium 13 (1998),
1-21. **

**79 (with R. Tijdeman)
****Irrationality criteria for numbers of Mahler's type****,
Analytic Number Theory ed. by Y. Motohashi, London Mathematical
Society Lecture Note Series 247 (1997), 341-351. **

**78 (with Noriko Hirata-Kohno) On the equation
$(x^m-1)/(x-1) = y^q$ with $x$ power, Analytic Number Theory ed.
by Y. Motohashi, London Mathematical Society Lecture Note Series 247
(1997), 119-125. **

**77 (with R. Balasubramanian) Perfect powers in
products of terms in an arithmetical progression (IV), Number
Theory, Contemporary Mathematics 210 (1997), 257-263, American
Mathematical Society. **

**76 (with R.Tijdeman) Some methods of Erd\"{o}s
applied to finite arithmetic progressions, The Mathematics of
Paul Erd\"os, ed. by Ronald L. Graham and Jaroslav
Ne\v{s}et\v{r}il, Springer (1997), 251-267. **

**75 (with R. Balasubramanian, M.
Langevin, and M. Waldschmidt) ****On the maximal length of two
sequences of integers in arithmetic progressions with the same prime
divisors****, Monatshefte f\"ur Mathematik 121 (1996),
295-307. **

**74 (with M. Mignotte) The equations $(x+1) \cdots
(x+k) = (y+1) \cdots (y+mk), m=5,6$, Indag. Math., N.S. 7 (1996),
215-225. **

**73 (with Yu.V. Nesterenko)
****Perfect powers in products of integers from a block of
consecutive integers (II)****, Acta Arith. 76 (1996), 191-198.
**

**72 Some applications of diophantine approximations to
diophantine equations, Number Theory, Paris 1993-4, ed. by S.
David, London Math. Soc. Lecture Note Series 235 (1996), 189-198. **

**71 Perfect powers in products of arithmetical
progressions with fixed initial term, Indag. Math., N.S. 7
(1996), 521-525. **

**70 (with N. Saradha and R.Tijdeman)
****On values of a polynomial at arithmetic progressions with
equal products****, Acta Arith. 72 (1995), 67-76. Correction
**

**69 (with N. Saradha and R.
Tijdeman) ****On the equation $x (x+1) \cdots (x+k-1) =
y(y+d)\cdots (y+(mk-1)d), \ \ m=1, 2,$**** Acta Arith. 71
(1995), 181-196. **

**68 (with N. Saradha and R. Tijdeman) On arithmetic
progressions of equal lengths with equal products, Math. Proc.
Camb. Phil. Soc. 117 (1995), 193-201. **

**67 On a conjecture that a product of $k$ consecutive
positive integers is never equal to a product of $mk$ consecutive
positive integers except for 8.9.10 =6! and related problems,
Number Theory, Paris 1992-3, ed. by S. David, London Math. Soc.
Lecture Note Series 215 (1995), 231-244. **

**66 (with N. Saradha and R.Tijdeman) On arithmetic
progressions with equal products, Acta Arith. 68 (1994), 89-100. **

**65 (with N. Saradha) On the equation $x(x+d_1) \cdots
(x+(k-1)d_1) = y(y+d_2) \cdots (y+(mk-1)d_2)$, Proc. Indian Acad.
Sci. (Math.Sci.) 104 (1994), 1-12. **

**64 (with R. Balasubramanian)
****Squares in products from a block of consecutive integers****,
Acta Arith. 65 (1994), 213-220. **

**63 Applications of Baker's theory of linear forms in
logarithms to exponential diophantine equations, Analytic Number
Theory, RIMS Kokyuroku 886 (1994), 48-60, Kyoto University. **

**62 (with R. Balasubramanian) On the equation $f(x+1)
\cdots f(x+k) = f(y+1) \cdots f(y+mk)$, Indag. Math., N.S.4
(1993), 257-267. **

**61 On the equation $x^{\ell}+y^{\ell}=2z^{\ell}$ and
related problems, Seminar on Number Theory, Caen 1992/93,
University of Caen, Exp. VI. **

**60 (with R. Tijdeman) On the greatest prime factor of
an arithmetical progression (III), Diophantine Approximation and
Transcendental Numbers, Luminy 1990, edited by Ph. Philippon, Walter
de Gruyter, New York (1992), 275-280. **

**59 (with R. Tijdeman) On the number of prime factors
of a finite arithmetical progression, Acta Arith. 61 (1992),
375-390. **

**58 (with R. Tijdeman) ****Perfect
powers in products of terms in an arithmetical progression (III)****,
Acta Arith. 61 (1992), 391-398. **

**57 (with R. Tijdeman) Perfect powers in products of
terms in an arithmetical progression (II), Compositio Math. 82
(1992), 119-136. **

**56 (with R. Tijdeman) Perfect powers in arithmetical
progression (II), Compositio Math. 82 (1992), 107-117. **

**55 (with N. Saradha) On the equation $x(x+d) \cdots
(x+(k-1)d) = y (y+d) \cdots (y+ (mk-1)d)$, Indag. Math., N.S.3
(1992), 237-242. **

**54 (with N. Saradha) On the equation $(x+1) \cdots
(x+k) = (y+1) \cdots (y+mk)$, Indag. Math., N.S.3 (1992), 79-90. **

**53 (with N. Saradha) The equations $(x+1) \cdots (x+k)
= (y+1) \cdots (y+mk)$ with $m=3,4,$ Indag. Math., N.S.2 (1991),
489-510. **

**52 (with R. Tijdeman) On the greatest prime factor of
an arithmetical progression, A Tribute to Paul Erdos, edited by
A. Baker, B. Bollobas and A. Hajnal, Cambridge University Press
(1990), 385-389. **

**51 (with K. Gyory and M. Mignotte) On some
arithmetical properties of weighted sums of $S-$units,
Mathematica Pannonica 1/2 (1990), 25-43. **

**50 (with R. Tijdeman) On the greatest prime factor of
an arithmetical progression (II), Acta Arith. 53 (1990), 499-504.
**

**49 (with N. Saradha) On the ratio of two blocks of
consecutive integers, Proc. Indian Acad. Sci. (Math. Sci.) 100
(1990), 107-132. **

**48 (with R. Tijdeman) Perfect powers in products of
terms in an arithmetical progression, Compositio Math. (1990),
307-344. **

**47 (with R. Balasubramanian and M. Waldschmidt) On the
maximal length of two sequences of consecutive integers with the same
prime divisors, Acta Mathematica Hungarica 54 (1989), 225-236. **

**46 (with R. Tijdeman) On the number of prime factors
of an arithmetical progression, Jour. Sichuan Univ. 26 (1989),
72-74. **

**45 Integers with identical digits, Acta Arith. 53
(1989), 81-99. **

**44 (with R. Tijdeman) Perfect powers in arithmetical
progression, Jour. Madras University (Section B) 51 (1988),
173-180. **

**43 (with K. Gyory) On the denominators of equivalent
algebraic numbers, Indag. Math. 50 (1988), 29-41. **

**42 Some exponential Diophantine equations II,
Number Theory and Related Topics ed. by\ S. Raghavan, Tata Institute
of Fundamental Research, Bombay (1988), 217-229. **

**41 Some exponential Diophantine equations, New
Advances in Transcendence Theory, ed. by A. Baker, Cambridge
University Press (1988), 352-365. **

**40 (with J.-H. Evertse, K. Gyory and R. Tijdeman) Equal
values of binary forms at integral points, Acta Arith. 48 (1987),
379-396. **

**39 (with Ram Murty and Kumar Murty) Odd values of
Ramanujan $\tau-$function, Bull. Soc. Math. France 115 (1987),
391-395. **

**38 (with C.L. Stewart) Pure powers in recurrence
sequences and some related Diophantine equations, Jour. Number
Theory 27 (1987), 324-352. **

**37 (with S. Srinivasan) Metrical results on square
free divisors of convergents of continued fractions, Bull. London
Math. Soc. 19 (1987), 135-138. **

**36 Ramanujan and binary recursive sequences, Jour.
Indian Math. Soc. 52 (1987), 147-157. **

**35 Perfect powers in products of integers from a block
of consecutive integers, Acta Arith. 49 (1987), 71-79. **

**34 Integer solutions of some equations, Current
Science 55, No.17 (1986), 815-817. **

**33 On the equation $ax^m-by^n=k$, Indag. Math. 48
(1986), 353-358. **

**32 On the equation $z^q=(x^n-1)/(x-1)$, Indag.
Math. 48 (1986), 345-351. **

**31 Perfect powers in values of certain polynomials at
integer points, Math. Proc. Camb. Phil. Soc. 99 (1986), 195-207. **

**30 (with M. Mignotte and R. Tijdeman) The distance
between terms of an algebraic recurrence sequence, Jour. Reine
Angew. Math. 349 (1984), 63-76. **

**29 On the ratio of values of a polynomial, Proc.
Indian \ Acad. Sci. (Math.Sci.) 93 (1984), 109-116. **

**28 On the equation $a(x^m-1)/(x-1) = b(y^n -1) /
(y-1)$ (II), Hardy Ramanujan Jour. 7 (1984), 1-10. **

**27 Linear forms in members of a binary recursive
sequence, Acta Arith. 43 (1984), 317-331. **

**26 (with C.L. Stewart) On the equation
$ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences,
Math. Scand. 52 (1983), 24-36. **

**25 Applications of linear forms in logarithms to
binary recursive sequences, Seminar on Number Theory, Paris
1981/82, Progr. Math. 38, Birkh$\tilde{a}$user, Boston (1983),
287-301. **

**24 Divisors of convergents of a continued fraction,
Jour. Number Theory 17 (1983), 127-133. **

**23 On the greatest square free factor of members of a
binary recursive sequence, Hardy-Ramanujan Jour. 6 (1983), 23-36.
**

**22 (with J.C. Parnami) Subsequences of binary
recursive sequences, Acta Arith. 40 (1982), 193-196. **

**21 The equation $ax^m+by^m=cx^n+dy^n,$ Acta Arith.
41 (1982), 255-260. **

**20 (with C.L. Stewart) On divisors of Fermat,
Fibonacci, Lucas and Lehmer numbers II, Jour. London Math. Soc.
(2) 23 (1981), 17-23. **

**19 (with R. Balasubramanian) On the equation
$a(x^m-1)/(x - 1)=b(y^n-1)/(y-1)$, Math. Scand. 46 (1980),
177-182. **

**18 On the greatest prime factor of $ax^m +by^n$,
Acta Arith. 36 (1980), 21-25. **

**17 (with A.J. van der Poorten, R. Tijdeman and A.
Schinzel) Applications of the Gel'fond-Baker method to Diophantine
equations, Transcendence Theory: Advances and Applications, ed.
by A. Baker and D.W. Masser, Academic Press, London (1977), 59-77. **

**16 (with K. Ramachandra and R. Tijdeman) On Grimm's
problem relating to factorisation of a block of consecutive integers
II, Jour. Reine \ Angew. Math. 288 (1976), 192-201. **

**15 (with R. Tijdeman) New applications of Diophantine
approximations to Diophantine equations, Math. Scand. 39 (1976),
5-18. **

**14 (with R. Tijdeman) On the greatest prime factors of
polynomials at integer points, Compositio \ Math. 33 (1976),
187-195. **

**13 (with P. Erd\"{o}s) On the greatest prime
factor of $2^p-1$ and other expressions, Acta Arith. 30 (1976),
257-265. **

**12 On linear forms in the logarithms of algebraic
numbers, Acta Arith. 30 (1976), 27-42. **

**11 Some applications of linear forms in logarithms,
Seminar Delange-Pisot-Poitou 1975/76, Paris, Exp. 28. **

**10 Some applications of linear forms in logarithms,
Seminar Delange - Pisot Poitou 1975/76, Paris, Exp.3. **

**9 (with K.Ramachandra and R. Tijdeman) On Grimm's
problem relating to factorisation of a block of consecutive integers,
Jour. Reine Angew. Math. 273 (1975), 109-124. **

**8 On the sum ${\displaystyle{\sum_{k=1}^{3}}} \mid
2^{\pi^k} -\alpha_k \mid, \alpha_k$ algebraic numbers, Jour.
Number Theory 6 (1974), 248-260. **

**7 Linear forms in the logarithms of algebraic numbers
with small coefficients II, Jour. Indian Math. Soc. 38 (1974),
285-292. **

**6 Linear forms in the logarithms of algebraic numbers
with small coefficients I, Jour. Indian Math. Soc. 38 (1974),
271-284. **

**5 On gaps between numbers with a large prime factor
II, Acta Arith. 25 (1974), 365-373. **

**4 (with K. Ramachandra) On gaps between numbers with a
large prime factor, Acta Arith. 24 (1973), 99-111. **

**3 $P-$adic analogue of a theorem of Tijdeman and its
applications, Indag. Math. 34 (1972), 436-442. **

**2 Algebraic independence of certain numbers in the
$P-$adic domain, Indag. Math. 34 (1972), 423-435. **

**1 On a theorem of Ramachandra, Acta Arith. 20
(1972), 215-221. **