I am being asked to factor $15347$ given that $7331^2 \equiv 1460^2 \pmod{15347}$. I've tried playing around with each of the numbers -- prime factorization, gcd, lcm, etc., but I can't find a connection that would help me factor $15347$. does anyone have a suggestion as to what to look for?
2026-03-30 10:56:29.1774868189
Using information from a congruence to factor a number
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Hint: $x^2 - y^2 = (x-y)(x+y)$. If the product of two numbers is $0$ (mod $n$), but neither is $0$ (mod $n$), what does that tell you?