Theoretical Statistics and Mathematics Unit, ISI Delhi

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]

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