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Same perfect square

Harry, Tom and I were each looking to find two 2-digit positive integers which each were the product of two primes and whose difference was also the product of two primes, the six primes all being different.

We each found a different valid solution; in each solution the sum of the two integers was a perfect square. For Harry and Tom it was the same perfect square.

What were my two integers?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 23 March. The Editor’s decision is final. Please send entries to Enigma 1633, New ÐÓ°ÉÔ­´´, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1627 THEBES = 542823

The winner Mike Waterman, Camberley, Surrey, UK