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How many positive integers $n$ satisfy $127 \equiv 18 \pmod{n}$?  ($n = 1$ is allowed.)

 Jun 27, 2024
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\( 127 \equiv 18 \pmod{n}\)

so 109 = 0 mod n

109 is prime so the only two solutions are \(\boxed{1\space and \space 109}\)

 Jun 27, 2024

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