Curious Numbers
Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.
math
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?
Solution
Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.
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