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4

Part of 2021 Austrian MO Beginners' Competition

Problems(1)

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

9/12/2021
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)
diophantineinequalitiesnumber theory