Question

A positive integer is said to be a prime if it is not divisible by any positive integer other than itself and one. Let P be a prime number strictly greater than $2$. Then, when $p^2+17$ is divided by $12$, the remainder is-

• A. $6$
• B. $1$
• C. $0$
• D. $8$

Answer 1

The correct option is A $6$

The square of any prime greater than $3$, when divided by $12$ leaves a remainder $1\cdot p^2$ when divided by $12$ leaves a remainder of $1$ and $17$ when divided by $12$ leaves a remainder of $5$. So $p^2+17$ when divided by $12$ leaves a remainder of $6$.