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Integers and Divisibility Challenge

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anemone

MHB POTW Director
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Feb 14, 2012
3,601
Prove that $\dfrac{378^3+392^3+1053^3}{2579}$ is an integer.
 
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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,601
Hint:

One can do some algebraic manipulation to the numerator and therefore factorize them.