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m> p if the diophantine p^2 + m^2 = n^2 holds for m,n pos. integers

Source: 2021 Austrian Mathematical Olympiad Junior Regional Competition , Problem 4

September 12, 2021
diophantineinequalitiesnumber theory

Problem Statement

Let pp be a prime number and let mm and nn be positive integers with p2+m2=n2p^2 + m^2 = n^2. Prove that m>pm> p.
(Karl Czakler)
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