Divisibility and converse statements

Number Theory Level 1

For integers $M$ and $N$ , the following is true:

If $M$ is divisible by $N$ , then $M^2$ must be divisible by $N$ .

However, the converse of this statement is not necessarily true.

Which of the following statements is false?

M^2

is divisible by 11, then

M

must be divisible by 11 If

M^2

is divisible by 12, then

M

must be divisible by 12 If

M^2

is divisible by 13, then

M

must be divisible by 13 If

M^2

is divisible by 14, then

M

must be divisible by 14

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