Some number theory problems:

1. Show that every integer of the form 6k+5 must also be of the form 3k+2

2. Show that the sqaure of any odd integer is of the form 8k+1

3. Prove that the cube of any integer can be written as one of 9k-1,9k or 9k+1

4. Prove that the sum of the squares of two odd integers cannot be a perfect square.

5. Prove that the difference of two consectutive cubes is odd.

Any help would be gratefully accepted.

Cheers

Cabouli