The Maths Item of the Month is a monthly problem aimed at teachers and students of GCSE and A level Mathematics. The problems can be used for enrichment, problem solving or as a way to encourage mathematical thinking/proof.

Consecutive pairs with no solo prime factors

$$675 = 3^3 \enspace\times\enspace 5^2$$ $$676 = 2^2 \enspace\times\enspace 13^2$$

Above are two examples of numbers in which each prime factor occurs to a power of at least 2.

Are there an infinite number of such consecutive pairs?

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