Question

Prove that for every integer n,
(n + 10)2≡n2(mod 20).

Answer 1

To prove that for every integer n, (n + 10)2 ≡ n2 (mod 20), we need to show that the two expressions have the same remainder when divided by 20.

Step-by-step explanation:

To prove that for every integer n, (n + 10)2 ≡ n2 (mod 20), we need to show that the two expressions have the same remainder when divided by 20.

Let's expand both expressions:

(n + 10)2 = n2 + 20n + 100

n2 (mod 20) = n2

The remainder when dividing both expressions by 20 is 0, therefore proving that (n + 10)2 ≡ n2 (mod 20).