Discrete Math Proof Prove by induction that if n is odd and

Discrete Math Proof:

Prove by induction that if n is odd and a is an element of N, then n^a is odd.

Solution

Prove by induction that if n is odd and a is an element of N, then n^a is odd

a is a natural number

let n be odd

n*n = n^2

n^2 is odd

n*n*n = n^3 = n^2*n = 0dd

therefore

n^(a-1) * n = n^a

which is odd always