Crowdly

Add to Chrome

Prove that if n is odd then n^2 + 5 \equiv 2 (mod 4 ).

✅ The verified answer to this question is available below. Our community-reviewed solutions help you understand the material better.

Prove that if n is odd then $n^2 + 5 \equiv 2$ n^2 + 5 \equiv 2 (mod 4).

Using the direct proof technique, we assume n is odd.

$n^2 + 5 \equiv 2$ n^2 + 5 \equiv 2 (mod 4)

proof

n^2 + 5 = (2k+1)^2 + 5 = 4k^2+4k+6 = 4(k^2+k+1) + 2

Using the EI rule, there is an integer k such that n=2k+1.

QED

The statement we need to prove is a universally quantified statement, so we consider an arbitrary integer n.

Get Unlimited Answers To Exam Questions - Install Crowdly Extension Now!

Add to Chrome