Publications

My Published and Papers in Press/Accepted Papers

1. Number of prime divisors in a product of consecutive integers (with T. N. Shorey), Acta Arith. 113 (2004), 327-341.
2. Number of prime divisors in a product of terms of an arithmetic progression (with T. N. Shorey), Indag. Math., 15(4) (2004), 505-521.
3. An estimate for the length of an arithmetic progression the product of whose terms is almost square, Pub. Math. Debrecen, 68 (2006), 451-475.
4. Greatest prime factor of a product of consecutive integers (with T. N. Shorey), Acta Arith., 120 (2005), 299-306.
5. The greatest prime divisor of a product of terms in an arithmetic progression (with T. N. Shorey), Indag. Math., 17(3) (2006), 425-436.
6. Grimm's Conjecture on consecutive integers, Int. Jour. Number Theory (with T. N. Shorey), 2 (2006), 207-211.
7. An extension of a theorem of Euler (with Hirata-Kohno, T. N. Shorey and R. Tijdeman), Acta Arith., 129 (2007), 71-102.
8. The equation n(n+d)...(n+(k-1)d) = by² with w(d) <= 6 or d <= 10¹⁰ (with T. N. Shorey), Acta Arith., 129 (2007), 249-305.
9. Squares in arithmetic progression with at most two terms omitted (with T. N. Shorey), Acta Arith., 134 (2008), 299-316.
10. Squares in products in arithmetic progression with at most one term omitted and common difference a prime power (with T. N. Shorey and Sz. Tengely), Acta Arith., 135 (2008), 143-158.
11. The number of prime divisors of consecutive integers, Jour. of Combinatorics and Number Theory (with R Balasubramanian, T. N. Shorey and R Thangadurai), 1 (3) (2009), 65-73.
12. On a conjecture on Ramanujan primes, Int. Jour. of Number Theory, 6 (2010), 1869-1873.
13. Irreducibility of generalised Hermite-Laguerre Polynomials II (with T. N. Shorey), Indag. Math., 20 (4) (2009), 427-434.
14. Some irreducibility results for truncated binomial expansions, Journal of Number Theory (with S.K. Khanduja and R. Khassa), 131 (2011) 300-308.
15. Stolarsky’s conjecture and the sum of digits of polynomial values (with K. Hare and T. Stoll), Proc. of the AMS, 1 (2011), 39-49.
16. On the sum of digits of n and n² (with K. Hare and T. Stoll), Int. Jour. of Number Theory, 7 (2011), 1737-1752.
17. Extensions of Schur’s irreducibility results (with T. N. Shorey), Indag. Math., 21 (2011), 87-105.
18. Solving n(n+d)...(n+(k-1)d) = by² with P(b) <= Ck (with M. Filaseta and N. Saradha), Int. Jour. of Number Theory, 8 (2012), 161-173.
19. Grimm’s Conjecture and smooth numbers (with R. Murty), Michigan Math. Journal, 61 (2012), 151-160.
20. Irreducibility of generalised Hermite-Laguerre Polynomials (with T. N. Shorey), Functiones et Approximatio, 47 (2012), 51-64.
21. Baker's Explicit abc-Conjecture and applications (with T. N. Shorey), Acta Arithmetica, 155 (2012), 419-429.
22. Fibonacci numbers of the form $x^a\pm x^b\pm 1$ (with F. Luca), Fibonnaci Quart., 52 (4) (2014), 290-295.
23. On the Galois groups of generalized Laguerre Polynomials Hardy Ramanujan Journal, 37 (2015), 8-12.
24. Powers in products of terms of Pell's and Pell-Lucas Sequences (with J. Bravo, P. Das and S. Guzman), Int. Jour. of Number Theory, 11 (2015), no. 4, 1259-1274.
25. Irreducibility of Generalized Laguerre Polynomials $L_n^{\frac{1}{2}+u}(x)$ with integer $u$ (with S. Nair and T. N. Shorey), Journal of Number Theory, 160 (2016), 76-107.
26. Power values of sums of products of consecutive integers (with L. Hajdu and S. Tengely), Acta Arith., 172 (2016), 333-349.
27. Rectangles of nonvisible lattice points (with F. Luca), Journal of Integer Sequences, 18 (2015) Article 15.10.8.
28. Perfect powers in Arithmetic Progression (with T. N. Shorey), Journal of Combinatorial Number Theory, 7 (2), 2016.
29. Baker's Explicit abc-Conjecture and Waring's problem, Hardy Ramanujan Journal, Hardy-Ramanujan Society, 2015, 38.
30. Irreducibility of generalized Hermite-Laguerre Polynomials III (with T. N. Shorey), Journal of Number Theory, 164 (2016), 303-322.
31. Perfect powers in products of terms of elliptic divisibility sequences (with L. Hajdu and M. Szikszai), Bulletin of Australian Math Soc., 94 (2016), 395-404.
32. Sums of the digits in bases 2 and 3 (with J-M Deshouillers, L. Habsieger and B. Landreau), Number Theory - Diophantine problems, Uniform Distribution and Applications - Festschrift in Honour of Robert F. Tichy's 60th Birthday", Ed. C. Elsholtz and P. Grabner, Springer (2017), 211-217.
33. Irreducibility and Galois Groups of Generalized Laguerre Polynomials $L_{n}^{(-1-n-r)}(x)$ (with A. Jindal and R. Sarma), J. Number Theory, 183 (2018), 388-406.
34. Variations of Erd\H{o}s- Selfridge superelliptic curves and their rational points (with P. Das and N. Saradha), Mathematika, 64 (2018), 380-386.
35. Cubes in products of terms from an arithmetic progression (with P. Das and N. Saradha), Acta Arith., 184 (2018), no. 2, 117-126.
36. Powerful numbers in product of consecutive integer values of a polynomial (with P. K. Dey), Publ. Math. Debrecen, 94 (2019).
37. Yet another generalization of Sylvester's Theorem and its application (with R. S. Moirangthem and S. S. Ngairangbam), Publ. Math. Debrecen, 95 (2019).
38. Progress towards a nonintegrality conjecture (with D. L\'opez-Aguayo, C. Pomerance and T. Thongjunthug), European Jour. of Math., (2019), https://doi.org/10.1007/s40879-019-00353-4.

39. On the Galois group of Generalised Laguerre polynomials II (with S. Nair and T. N. Shorey), Hardy Ramanujan Journal, 42 (2019), 26-30.
40. Irreducibility of extensions of Laguerre Polynomials (with S. Nair and T. N. Shorey), Funct. Approx. Comment. Math., 62 (2020), no. 2, 143–164.
41. On members of Lucas sequences which are products of factorials (with F. Luca and M. Sias), Monatsh. Math., 193 (2020), 329–359.
42. On members of Lucas sequences which are products of Catalan numbers (with F. Luca and M. Sias), Int. Jour. Number Theory, https://doi.org/10.1142/S1793042121500457.

Publications

Submitted Papers and Preprints

Some Solutions