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In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation
satisfying x > y > 1 {\displaystyle x>y>1} and n , m > 2 {\displaystyle n,m>2} are
and
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