2. (a) if ged(a, 35) = 1, show that a = 1 (mod 35). [hint: from fermat's theorem a = 1 (mod 7) and at = 1 (mod 5).] b f ged(a, 42) = 1, show that 168 = 3.7.8 divides aº - 1. (c) if geda, 133) = ged(b, 133) = 1, show that 133 a18 - 18. 3. from fermat's theorem deduce that, for any integer n > 0,131112n+6 +1. 4. derive each of the following congruences: (a) a = a (mod 15) for all a. [hint: by fermat's theorem, a' = a (mod 5).] (b) a' = a (mod 42) for all a. (c)' = a (mod 3. 7. 13) for all a. 9 20) fe