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Random Interesting Patterns Followed by Square Numbers

Three consecu...

Question

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum value, say m, of these three integers? (CAT 2008)

A

1<=m<=3

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B

4<=m<=6

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C

10

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D

13<=m<=15

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Solution

The correct option is A 1<=m<=3
It's an easy question. Hit and trial with some numbers will give us the solution.
$1 \leq m \leq 3$
$3^{1} + 4^{2} + 5^{3} = 144 = 12^{2} = (3 + 4 + 5)^{2} .$

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