Question

Prove the following statement: The sum of any two consecutive integers can be written in the form 4n+1 for some integer n.

Answer 1

Not true

All I need is one exception to your "rule"
e.g. take the first 2 positive integers,
1 + 2 = 3,
4n+1 = 3
4n = 2
n = 1/2, but n was supposed to be an integer, so ..... false