I'm using Wilson's Theorem to find the remainder of 24! when divided by 29. Here are my steps thus far:
24!*25*26*27*28 ≡ -1 mod 29
24!*(-4)*(-3)*(-2)*(-1) ≡ -1 mod 29
24!*24 ≡ -1 mod 29
How do I finish off the congruency to find the remainder?
That's a good start. In fact, you're nearly there. Next step is to say that 24 ≡ –5 (mod 29), so 24!*5 ≡ 1 (mod 29). Finally 5*6 = 30 ≡ 1 (mod 29), so multiply both sides by 6 and you finish with 24! ≡ 6 (mod 29).