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Primes and Six

Age 14 to 16 Short
Challenge Level

Let $p$ and $q$ be prime numbers with $q=p+2$ and $p$ greater than $3$.

Prove that $pq+1$ is divisible by $36$.

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.