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A note on the products ((m+1)(2)+1)((m+2)(2)+1) ... (n(2)+1) and ((m+1)(3)+1)((m+2)(3)+1) ... (n(3)+1)

2016-05-01
Gurel, Erhan
We prove that for any positive integer m there exists a positive real number N-m such that whenever the integer n >= m neither the product P-m(n) = ((m + 1)(2) + 1) ((m + 2)(2) + 1) ... (n(2) + 1) nor the product Q(m)(n) = ((m + 1)(3) + 1)((m + 2)(3) + 1) ... (n(3) + 1) is a square.