2000 OIM Problems/Problem 3

Problem

Find all solutions to the equation

\[(x + 1)^y - x^z = 1\]

for $x, y, z$ integers greater than 1.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe15.htm