Dirisibly Yours

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.
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Problem



We wonder who can find and explain the shortest and neatest proof that

$5^{2n+1} + 11^{2n+1} + 17^{2n+1}$

is divisible by 33 for every non negative integer n .