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Number Theory Level 3

If $n$ is a positive integer, then find the number of $n$ for which the congruence $1+1 \equiv 23 \pmod{n}$ holds true.

1 solution

Nihar Mahajan
Jun 1, 2015

$2 \equiv 23 \pmod{n} \\ \Rightarrow n | -21$

Positive divisors of $-21 \ are \ 1,3,7,21$ .This means number of $n$ satisfying the congruence are $\boxed{4}$ .

Sweet and short! +1

Sravanth C. - 6 years ago