Prove that the square of any odd integer is of the form 8n+1

Question

Mathematics

Lewis Garner

25 October, 16:40

Prove that the square of any odd integer is of the form 8n+1

+3

Answers (1)

Know the Answer?

Aidan Zavala · Answer 1

For any integer x,

if x is even, then

x^2+x = (2k) ^2 + 2k = 2 (2k^2 + k) is even

if x is odd, then

x^2+x = (2k+1) ^2 + 2k+1 = 2 (2k^2 + 3k + 1) is also even.

When x is odd,

x^2 = (2k+1) ^2 = 4 (k^2+k) + 1 = 4 (2n) + 1 = 8n+1