examday

/TMUA

The result $21=3\times7$ can be used as a counterexample to how many of the following statements involving an integer $p$?

• $p+1$ is always a multiple of $5$ when $p$ is even
• when $p$ is even, $p^2$ is always a multiple of $5$
• if $p$ is a multiple of $3$, it is also a multiple of $5$
• when $p$ is prime, it is never a multiple of $7$
• when $p$ is not prime it is always a product of $2$ primes