Find n ∈ {1, 2, 3, . . . , 28} that satisfies 26! ≡ n (mod 29).

Prove that (50!)2 mod 101 = -1 mod 101.

11. Show that 2 (p - 3)! + 1 = 0 (mod p).

Suppose that a and b are integers, a = 4 (mod 7) and b = 6 (mod 7). Find the integer c with 0 ≤ c ≤ 6 such that: a. c = 3a (mod 7) b. c = 5b (mod 7) c. c = 2a + 4b (mod 7) d. ca²b² (mod 7)

3. Find all integer solutions to the pair of congruences (if any) x = 1 (mod 2) * = 2 (mod3) x = 3 (mod 5) x = 4 (mod 11)

4. Prove that if a = b (mod n) and m/n, then a = b (mod m)...

4 ≡≡              (mod 8)