(562) 3

Part of 1997 Tournament Of Towns

Problems(1)

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

Source:

All expressions of the form

\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)

number theoryIntegerPerfect Square