prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.

2. Originally Posted by bearej50
prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
Think about the ways that you can express n as an even integer and as an odd integer. To start, for y = 0, n = 2x accounts for all even integers...

3. Prove by induction.

Base Case is fairly easy.

The inductive step is done in two parts.
i) When x>0 (replace x by x-1 and y by y+1 and you have n+1)
ii) When x=0 (replace y by y-1 and x by x+2 and you have n+1)

4. Originally Posted by bearej50
prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
If $n$ is even then we can write $n = 2x$. If $n>2$ is odd then $n-3$ is even and then $n-3=2x\implies n = 2x + 3$.