A number leaves remainder 3 when divided by 5. What is the remainder when its square is divided by 5?

Given data

• n ≡ 3 (mod 5)

Concept / Approach

• Use modular arithmetic: square both sides of a congruence.

Step-by-step calculation

n^2 ≡ 3^2 = 9 ≡ 4 (mod 5)

Check via examples

n = 3, 8, 13, … ⇒ n^2 = 9, 64, 169, … ⇒ remainders mod 5 are 4.

Final Answer

Remainder = 4.