Proving/Disproving: Coprimes & (an + bn + cn ) / abc

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mahmudarif
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if a, b, c (integers) are coprimes then (an + bn + cn ) / abc can't be a number that is not a fraction (integer). Any idea to prove/disprove it will be highly appreciated.
 
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If the sum is divisibleby abc what does that say about the terms