In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh about the solutions of the exponential Diophantine equation x m − 1 x − 1 = y n − 1 y − 1 {\displaystyle {\frac {x^{m}-1}{x-1}}={\frac {y^{n}-1}{y-1}}} with distinct integers x , y {\displaystyle x,y} larger than one and exponents larger than two. One convention is x > y > 1 {\displaystyle x>y>1} and in turn n > m > 2 {\displaystyle n>m>2} .
In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh about the solutions of the exponential Diophantine equation x m − 1 x − 1 = y n − 1 y − 1 {\displaystyle {\frac {x^{m}-1}{x-1}}={\frac {y^{n}-1}{y-1}}} with distinct integers x , y {\displaystyle x,y} larger than one and exponents larger than two. One convention is x > y > 1 {\displaystyle x>y>1} and in turn n > m > 2 {\displaystyle n>m>2} .
Source: Wikipedia "Goormaghtigh conjecture" · CC BY-SA 4.0
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