# Pairs of Perfect Squares

Number Theory Level 5

Determine the sum of all positive integers $$N \leq 100$$ such that when the digits of $$N^2$$ are each increased by 3, the new number is a perfect square.

Details and assumptions

There is no carryover allowed. It is an implicit assumption that the individual digits of $$N^2$$ are all $$\leq 6$$.

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