# Publications and Preprints

Perfect powers in Arithmetic Progression}
by
Shanta Laishram and T. N. Shorey
The conjecture of Masser-Oesterl\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve the equation \begin{equation*} n(n+d)\cdots(n+(k-1)d)=by^l \end{equation*} in positive integer variables $n, d, k, b, y, l$ such that $b$ square free with the largest prime divisor of $b$ at most $k$, $k\geq 2, l\geq 2$ and gcd$(n, d)=1$.

isid/ms/2015/18 [fulltext]