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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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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