Question

Consider the following statements. For any integer n.
I. $n^2+3$ is never divisible by $17$.
II. $n^2+4$ is never divisible by $17$. then.

• A. Both I and II are true
• B. Both I and II are false
• C. I is false and II is true
• D. I is true and II is false

Answer 1

The correct option is D I is true and II is false

$n^2+4$ can be written as

$\Rightarrow (k+8{)}^2+4=k^2+16k+68$($\because$ we know that $68$ is divisible by $7$ )

$=k(k+16)+68$ is divisible by $17$ if $k$ or $(k+16)$ is divisible by $17$. but $n^2+3$ cannot be written in the form of $17$'s multiple.

Thus, statement | is true and statement || is false.