CURIOUS NUMBERS.
(
Money Puzzles)
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?
Answer:
The three smallest numbers, in addition to 48, are 1,680, 57,120, and
1,940,448. It will be found that 1,681 and 841, 57,121 and 28,561,
1,940,449 and 970,225, are respectively the squares of 41 and 29, 239
and 169, 1,393 and 985.
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