6

Part of 2005 China National Olympiad

Problems(1)

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

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

Find all nonnegative integer solutions

(x,y,z,w)

of the equation

2^x\cdot3^y-5^z\cdot7^w=1.

modular arithmeticnumber theoryrelatively primeDiophantine equationZsigmondy