Question 17
Given a positive integer $n \ge 4$, prove that the equation
$$
(2^x - 1)(5^x - 1) = y^n
$$
has no positive integer solutions $(x, y)$.
$$
(2^x - 1)(5^x - 1) = y^n
$$
has no positive integer solutions $(x, y)$.
MathNet 2025-part-01 — 187 problems (EN–VI) Question 17
Math Olympiad Vault · MathNet 2025-part-01 — 187 problems (EN–VI)