Proof by Contradiction Question

Question

use proof by contradiction to show that for all real numbers n, if n mod 6=1, then mod 4 ≠2

Answer 1

I assume you mean n mod 4 <> 2

Assume n mod 4 = 2

Then n = 4k + 2, where k is an integer

And n mod 6 = 1 means n = 6l + 1, where l is an integer

4k + 2 = 6l + 1

2-1 = 6l - 4k

1 = 2 (3l-2k)

The left is odd , and the right is even as it is divisible by 2, so this is impossible.

Therefore n mod 4 can't be 2,