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TOT 562 1997 Autumn S A3 \pi \sqrt1 \pm \sqrt2 \pm ... \pm \sqrt{100}

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September 11, 2024
number theoryIntegerPerfect Square

Problem Statement

All expressions of the form ±1±2±...±100\pm \sqrt1 \pm \sqrt2 \pm ... \pm \sqrt{100} (with every possible combination of signs) are multiplied together. Prove that the result is: (a) an integer; (b) the square of an integer.
(A Kanel)
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