Squares in products in arithmetic progression with at most one term omitted and common difference a prime power

Abstract

It is shown that a product of k−1 terms out of k ≥ 7 terms in arithmetic progression with common difference a prime power >1 is not a square. In fact it is not of the form by 2 where the greatest prime factor of b is less than or equal to k. Also, we show that product of 11 or more terms in an arithmetic progression with common difference a prime power > 1 is not of the form by 2 where the greatest prime factor of b is less than or equal to p π(k)+2 .