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Sum of two squares, equation

Source: 54 Polish MO 2003 Second Round - Second Day Problem 4

April 21, 2018
number theorycombinatoricsCombinatorial Number TheoryPolandpigeonhole principleprime numbers

Problem Statement

Prove that for any prime number p>3p > 3 exist integers x,y,kx, y, k that meet conditions: 0<2k<p0 < 2k < p and kp+3=x2+y2kp + 3 = x^2 + y^2.
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