(2) Apply the Euclid's Algorithm to find integer pairs p, q such that (a) ged(225,65) = 225p+65q (b) ged(354, 123) = 354p+123q == (3) Show that if a = b ( mod m) and a = c( mod n) then b=c( mod d) where d = gcd (m, n). (4) Show that whenever n is an odd integer, 3n + 13 is even. (5) (a) Let n be an integer. Show that 2n2+1=0 (mod 3) or 2n +1=1 (mod 3). (b) Let n be an integer. Show that 2n2+1=1 (mod 5) or 2n2+1=3 (mod 5) or 2n2+1=4 (mod 5).