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

Source: Turkey JBMO TST 2024 P5

May 13, 2024
number theoryDivisibilityPerfect Squares

Problem Statement

Find all positive integer values of nn such that the value of the 2n!−12n−1\frac{2^{n!}-1}{2^n-1} is a square of an integer.
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