IBM Ponder This #225 · January 2017

There is exactly one integer solution for 0<x<y, x^y=y^x.

Hertsel Amrani (thanks!) asked me about rational solutions and inspired the idea for this month's challenge, which is to find a rational solution for x^y=y^x, where the last eight digits of x are different from each other.

Supply your answer as a formula for x and y, and the first and last 10 digits of x and y.

Solution

Best opened after a real attempt

To be added.