Correct Answer - Option 1 : 1
Given:
If a positive integer 'n' is divided by 15, the remainder is 4.
Concept used:
Dividend = (Divisor × Quotient) + Remainder
Calculation:
Let the quotient be ‘a’
According to the question,
⇒ n = (15 × a) + 4
Square both sides
⇒ n2 = [(15 × a) + 4]2
⇒ n2 = (15a + 4)2
⇒ n2 = 225a2 + 120a + 16
⇒ n2 = 225a + 120a + 16
⇒ n2 = 15(15a + 8) + 16
On comparing with (Dividend = (Divisor × Quotient) + Remainder)
⇒ Remainder = 1
∴ 1 is the remainder when n2 is divided by 15.