Question 55
Let $n \gt 3$ be a positive integer. Define an integer $k$ to be snug if $1 \leq k \lt n$ and
$$
\gcd(k, n) = \gcd(k+1, n).
$$
Prove that the product of all snug integers is congruent to $1$ modulo $n$.
$$
\gcd(k, n) = \gcd(k+1, n).
$$
Prove that the product of all snug integers is congruent to $1$ modulo $n$.