+537 For how many integers a satisfying \(1 \le a \le 23\) is it true that \(a^{-1} \equiv a \pmod{24}\)?
+6251 \(a^{-1}\equiv a \pmod{24} \Longleftrightarrow a^2 \equiv 1 \pmod{24}\\ a^2-1 = 24k,~k \in \mathbb{Z}\)
\(|\{1,5,7,11,13,17,19,23\}|=8\)
\(\text{We notice that these are primes such that }p^2 > 24\\ \text{There must be an algebraic reason for this and I'll see if I can dig it up}\)
.+6251 \(a^{-1}\equiv a \pmod{24} \Longleftrightarrow a^2 \equiv 1 \pmod{24}\\ a^2-1 = 24k,~k \in \mathbb{Z}\)
\(|\{1,5,7,11,13,17,19,23\}|=8\)
\(\text{We notice that these are primes such that }p^2 > 24\\ \text{There must be an algebraic reason for this and I'll see if I can dig it up}\)
