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Existence of a solution of a diophantine equation

Source: North Korea Team Selection Test 2013 #6

May 17, 2014
inductionnumber theory proposednumber theory

Problem Statement

Show that x3+x+a2=y2 x^3 + x+ a^2 = y^2 has at least one pair of positive integer solution (x,y) (x,y) for each positive integer a a .
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