Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is A $1$

Any prime number greater then $3$ can be written in form of $6n+1$ or $6n-1$

$\Rightarrow$ Now, ${(6n+1)}^2=36n^2+1+12n$

$=3(12n^2+4n)+1$

Or it shall be $1$ similarly,

$\Rightarrow {(6n+1)}^2=3(12n^2+4n)+1$

So, the remainder is $1.$

Hence, the answer is $1.$