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A Note on the Diophantine Equation x! + A = y^2, II

Alain Togbé

Abstract


In this note, we study the variant of the Brocard-Ramanujan Diophantine equation x! + A = y^2. In a previous note, we studied a system of three equations of the type Brocard-Ramanujan. First, we consider another pattern, precisely the cases A = 4k + 3, A =4(k + 1) + 3, A = 4(k + 2), where kЄN. We prove that these simultaneous equations have only two integral solutions. Then we show that the set of |A| is of asymptotic density zero.

Keywords


Brocard-Ramanujan, Diophantine equation

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