Friday, 1 August 2014

Divisible by Five

Show that if the sum of the fifth powers of five integers is divisible by 25
then one of the original integers is divisible by five.
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Define f:R→R by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...