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

Answer 1

The correct option is A 1

Any prime number greater than 3 is of the form 6k $\pm$ 1, where k is a natural number.

$\Rightarrow$ Square of any prime number greater than 3
$=(6k\pm 1{)}^2$
$=36k^2\pm 12k+1$
$=6k(6k\pm 2)+1$

$\therefore$ When the square of any prime number greater than 3 is divided by 6, the remainder is 1.