Diophantine equations in separated variables and polynomial power sums
Diophantine equations in separated variables and polynomial power sums
Abstract We consider Diophantine equations of the shape $$ f(x) = g(y) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> <mml:mo>(</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove …