Testwiki:Reference desk/Archives/Mathematics/2025 January 23

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January 23

Given an integer for which a square root against a large semiprime modulus exists, is the number of possible square roots always 4 ?

Simple question : take a large semiprime $n$. Take an integer $i$ such as √i%n has an existing solution. Is the number of possible solutions always 4 in such a case ? (or 2 if the modular inverse are excluded) 2A01:E0A:401:A7C0:E4AA:FB65:CDCC:FA58 (talk) 11:09, 23 January 2025 (UTC)

Yes, because 1 always has four square roots modulo an (odd) semiprime. Tito Omburo (talk) 12:11, 23 January 2025 (UTC)