For any integer n > 1, the canonical form of n is given by n = pi'p*p -· PR where p;'s are primes n = PIP2P3 Pk where p,'s are primes n = 2P – 1 where p is prime n = (p – 1)(p +1) where p is prime

Let p=17. If a belongs to F_{17} and a is non zero , compute the value of a^{16}(mod 17) for a=3 .

Prove by induction that (1+1/5)^n ≥ 1 + n/5 for all n∈N∪{0}.

Let n > 3 and 2 (;) ')<(3) k n – k + + in two ways: (a) algebraic proof, and (b) combinatorial proof Hint for (b): show that the left side counts only some of the things counted by the right side.