The number $48$ has this peculiarity, that if you add $1$ to it the result is a square number ($49,$ the square of $7$), and if you add $1$ to its half, you also get a square number ($25,$ the square of $5$). Now, there is no limit to the numbers that have this peculiarity, and it is an interesting puzzle to find three more of them—the smallest possible numbers. What are they?
Solutions: 1
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