k ≡ 0 (mod m) means k is a multiple of m.
Since m is not prime, it has at least one pair of factors, a * b = m.
a < m and b < m
(m-1)! = 1 * 2 * 3... * a ... * b ... * (m-1) is a multiple of (a*b), so it is a multiple of m.
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k ≡ 0 (mod m) means k is a multiple of m.
Since m is not prime, it has at least one pair of factors, a * b = m.
a < m and b < m
(m-1)! = 1 * 2 * 3... * a ... * b ... * (m-1) is a multiple of (a*b), so it is a multiple of m.