Question

Prove that for all integers n, if n^(2)-6n is odd then n is odd.

Answer 1

Explanation:

o - odd number

e - even number

n × e = e, n is either odd or even...rule 1

n - e = o, n must be odd...rule 2

n - e = e, n must be even...rule 3

n^2 = o, n must be odd...rule 4

n^2 = e, n must be even...rule 5

6n is even, no matter if n is odd or even following rule 1

if n^2 - 6n = o, n must be odd following rule 2

if n^2 = o, n must be odd following rule 4