Prove that if the square of a whole number is added to the same whole number, the sum will be an even number.

n=the whole number

n2=the square of the whole number

n2+n=the sum

proof:

n2+n the sum

n (n+1) factored

for all whole numbers n, n and n+1 are consecutive whole numbers

for any two consecutive whole numbers, one must be even and one must be odd

the product of an even number and an odd number is always an even number

therefore n2+n is an even number