5

Part of 2024 JBMO TST - Turkey

Problems(1)

\frac{2^{n!}-1}{2^n-1} be a square

Source: Turkey JBMO TST 2024 P5

Find all positive integer values of

n

such that the value of the

\frac{2^{n!}-1}{2^n-1}

is a square of an integer.

number theoryDivisibilityPerfect Squares