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Question 11

The number of pairs of two-digit square numbers whose sum or difference is also a square is

Solution

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The two-digit squares are $$16,25,36,49,64,81$$. We have $$25-16=9$$ and $$36+64=100$$, both of which are squares. Checking the remaining pairs gives no other square sum or difference, so there are $$2$$ pairs.

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