Enigma 1633: Same perfect square
12 December 2011
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From New Scientist #2799, 12th February 2011 [link]
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?