T.N. Shorey's Home Page

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Publications

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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.

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.

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

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

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.

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

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

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

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