1. Decide if the following statements are TRUE or FASLE. If FALSE, explain why}.r it is FALSE or give a counter example (a) If ax + by = 2 for some integers x, y then god (a, b) = 2. {b} For any integer b there exist unique integers q, r with b = To + \"r and 3 :1 r E 3. (o) If ale and blc, then lorn(a, b)|c. (d) If (III? and le, then able. (-3) 93 E 3 (mod 15) (f) lfx is odd then x2 E 1 (mod 4) (g) god (3a -| 1, 2a 3) = 5 for infinitely many a. (11} lfp is a prime and 1:32ln3 then pzlo. (i) lfx E 31\".} (mod F) then x E [mod 21) [j] The equation 15x E 21 (mod 35) has Ssolutions mod 35