Hello, the undertaker!

I baby-talked my way through it . . .

Prove that if are odd integers,

then: . .has no integer roots.

Note that:

An even integer raised to any positive integral power is even: .

An odd integer raised to any positive integral power is odd: .

We have: .

Suppose is even.

We have: .

. . . . . . . . .

And the difference of an even number and an odd number canbe zero.not

Suppose is odd.

We have: .

. . . . . . . . .

And the difference of an odd number and an even number canbe zero.not