3. From Fermat's theorem deduce that, for any integer n 0, 13 | 1112n+6 +1. 4. Derive each of the following congruences: (a) a21a (mod 15) for all a. 4. Derive each of the following congruences: (a) a1 = a (mod 15) for all a. [Hint: By Fermat's theorem, a5 = a (mod 5).] (b) a = a (mod 42) for all a. 13 (c) a 3 = a (mod 3.7. 13) for all a. (d) a = a (mod 30) for all a. 5. If ged(a, 30) = 1, show that 60 divides a +59. 6 (2) Find the 1: 62100 T