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in Olympiad by (76.3k points)

Show that there are infinitely many triples (x, y, z) of integers such that x3 + y4 = z31.

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x3 + y4 = z11 

Let x = 0 => y4 = z11 => y = z11/4 (many values of z of the form (integer)4 will give integral values of y. so infinite sets.

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