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The equation:
x m − 1 x − 1 = y n − 1 y − 1 {\displaystyle {\frac {x^{m}-1}{x-1}}={\frac {y^{n}-1}{y-1}}} ,
has the following integer solutions for x , y > 1 {\displaystyle x,y>1} and m , n > 2 {\displaystyle m,n>2} :
,
and 
:
.
.