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n + 1 is the sum of p perfect squares if pn + 1 is a perfect square

Source: IV - Rioplatense 1995 L3 P1

September 19, 2022
number theoryPerfect Square

Problem Statement

Let nn and pp be two integers with pp positive prime, such that pn+1pn + 1 is a perfect square. Show that n+1n + 1 is the sum of pp perfect squares, not necessarily distinct.
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