Prove that if m and n are odd integers, then is divisible by 16.
Hello, Sigyn3!
I used your approach, Jhevon . . . and hit a wall.Prove that, if and are odd integers, then is divisible by 16.
We have: .
Let .
Then:. .
. . . . . .
And we have: .
. . . . . . . . . .
So we have a multiple of 8.
. . And here's where I hit the wall . . .
I tried various ways to find another factor of 2,
. . and settled on an exhaustive listing.
. .
So for any combination of and , at least one of the factors is even.
Therefore, is a multiple of 16.
Surely there must a more elegant method . . .
.