Publications
My Published and Accepted Papers
- Number of prime divisors in a product of consecutive integers (with T. N. Shorey), Acta Arith. 113 (2004), 327-341.
- Number of prime divisors in a product of terms of an arithmetic progression (with T. N. Shorey), Indag. Math., 15(4) (2004), 505-521.
- An estimate for the length of an arithmetic progression the product of whose terms is almost square, Pub. Math. Debrecen, 68 (2006), 451-475.
- Greatest prime factor of a product of consecutive integers (with T. N. Shorey), Acta Arith., 120 (2005), 299-306.
- The greatest prime divisor of a product of terms in an arithmetic progression (with T. N. Shorey), Indag. Math., 17(3) (2006), 425-436.
- Grimm's Conjecture on consecutive integers, Int. Jour. Number Theory (with T. N. Shorey), 2 (2006), 207-211.
- An extension of a theorem of Euler (with Hirata-Kohno, T. N. Shorey and R. Tijdeman), Acta Arith., 129 (2007), 71-102.
- 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.
- Squares in arithmetic progression with at most two terms omitted (with T. N. Shorey), Acta Arith., 134 (2008), 299-316.
- 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.
- 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.
- On a conjecture on Ramanujan primes, Int. Jour. of Number Theory, 6 (2010), 1869-1873.
- Irreducibility of generalised Hermite-Laguerre Polynomials II (with T. N. Shorey), Indag. Math., 20 (4) (2009), 427-434.
- Some irreducibility results for truncated binomial expansions, Journal of Number Theory (with S.K. Khanduja and R. Khassa), 131 (2011) 300-308.
- 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.
- On the sum of digits of n and n2 (with K. Hare and T. Stoll), Int. Jour. of Number Theory, 7 (2011), 1737-1752.
- Extensions of Schur’s irreducibility results (with T. N. Shorey), Indag. Math., 21 (2011), 87-105.
- 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.
- Grimm’s Conjecture and smooth numbers (with R. Murty), Michigan Math. Journal, in press.
- Irreducibility of generalised Hermite-Laguerre Polynomials (with T. N. Shorey), Approx. Commentarii Mathematici, in press.
Submitted Papers, Preprints and in preparation
Some Solutions
- American Mathematical Monthly(AMM) Problem #10893
- Mathematics Magazine Problem (with Ritumoni Sarma) #1626