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2^x * 3^y - 5^z * 7^w = 1

Source: china mathematical olympiad cmo 2005 final round - Problem 6

January 25, 2005
modular arithmeticnumber theoryrelatively primeDiophantine equationZsigmondy

Problem Statement

Find all nonnegative integer solutions (x,y,z,w)(x,y,z,w) of the equation2x⋅3y−5z⋅7w=1.2^x\cdot3^y-5^z\cdot7^w=1.
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