On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases

In 1956, Jes´manowicz conjectured that for any primitive Pythagorean triple (a, b, c) with the Diophantine equation a2 + b2 = c2 and any positive integer k, the only solution of equation (ak)x +(bk)y = (ck)z, in positive integers, is (x, y, z) = (2, 2, 2). It is a famous unsolved conjecture on Pytha...

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