Prove all of the following statements Please explain step by

Prove all of the following statements. Please explain step by step (True or False)

Solution

1. Every positive integer will be one of the form 3k, 3k+1, 3k+2, for some integer k.

If n=3k, then 3| n

If n=3k+1, n+2= 3k+1+2=3k+3=3(k+1)

3| n+2

If n= 3k+2, n+4 = 3k+2+4= 3k+6=3(k+2)

3| n+4

so in any case, 3 | n or 3| n+2 or n| n+4