Question

The remainder when the square of any prime number greater than 3 is divided by 6, is

(a) 1
(b) 3
(c) 2
(d) 4

[Hint: Any prime number greater than 3 is of the from 6k ± 1, where k is a natural number and (6k ± 1)² = 36k² ± 12k + 1 = 6k(6k ± 2) + 1]

Answer 1

Any prime number greater than 3 is of the form, where k is a natural number.

Thus,

When, is divided by 6, we get, and remainder as 1.

Hence, the correct choice is (a).