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.