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x-831-y-831-is-always-divisible-by-

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Question Number 9166 by nazar last updated on 21/Nov/16
x^(831) + y^(831) is always divisible by
x831+y831isalwaysdivisibleby
Commented by prakash jain last updated on 22/Nov/16
put x=−y (−y)^(831) +y^(831) =0 Hence x+y is factor of x^(831) +y^(831)
putx=−y(−y)831+y831=0Hencex+yisfactorofx831+y831
Answered by RasheedSoomro last updated on 22/Nov/16
x^(831) +y^(831) =(x^(277) )^3 +(y^(277) )^3 =(x^(277) +y^(277) )(x^(554) −x^(277) y^(277) +y^(554) ) Hence x^(831) +y^(831) is always divisible by x^(277) +y^(277) , x^(554) −x^(277) y^(277) +y^(554) and x^(831) +y^(831) (itself)
x831+y831=(x277)3+(y277)3=(x277+y277)(x554−x277y277+y554)Hencex831+y831isalwaysdivisiblebyx277+y277,x554−x277y277+y554andx831+y831(itself)

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