Multiple choice general knowledge math & puzzles

Which is the only positive whole number,less than 15 that can't be represented as the sum of the squares of any three integers.?

  1. 3

  2. 2

  3. 7

  4. 1
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C Correct answer
Explanation

By Legendre's three-square theorem, a positive integer n can be expressed as the sum of three squares of integers if and only if n is not of the form 4^a(8b+7) for nonnegative integers a and b. Testing numbers 1-14, only 7 satisfies this condition (7 = 4^0 × (8×0+7)), making it impossible to represent as a sum of three squares. All other numbers like 1 (= 1²+0²+0²), 2 (= 1²+1²+0²), and 3 (= 1²+1²+1²) can be represented.

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