Remainder for equation with multi-variable











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I was trying to figure out the remiander when $(a+b+c)^{333}-a^{333}-b^{333}-c^{333}$ is devided by $(a+b+c)^3-a^3-b^3-c^3$.



I first tried to factor them but this guy don't factor in any nice way. I don't know much number theory. I think moduler arithmetic might help. But I don't know that properly either. Can some one please help me out?






abstract-algebra number-theory chinese-remainder-theorem







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  • math.stackexchange.com/questions/288965/…
    – lab bhattacharjee
    22 hours ago















up vote
2
down vote

favorite
2












I was trying to figure out the remiander when $(a+b+c)^{333}-a^{333}-b^{333}-c^{333}$ is devided by $(a+b+c)^3-a^3-b^3-c^3$.



I first tried to factor them but this guy don't factor in any nice way. I don't know much number theory. I think moduler arithmetic might help. But I don't know that properly either. Can some one please help me out?






abstract-algebra number-theory chinese-remainder-theorem







share|cite|improve this question
























  • math.stackexchange.com/questions/288965/…
    – lab bhattacharjee
    22 hours ago













up vote
2
down vote

favorite
2









up vote
2
down vote

favorite
2






2





I was trying to figure out the remiander when $(a+b+c)^{333}-a^{333}-b^{333}-c^{333}$ is devided by $(a+b+c)^3-a^3-b^3-c^3$.



I first tried to factor them but this guy don't factor in any nice way. I don't know much number theory. I think moduler arithmetic might help. But I don't know that properly either. Can some one please help me out?






abstract-algebra number-theory chinese-remainder-theorem







share|cite|improve this question















I was trying to figure out the remiander when $(a+b+c)^{333}-a^{333}-b^{333}-c^{333}$ is devided by $(a+b+c)^3-a^3-b^3-c^3$.



I first tried to factor them but this guy don't factor in any nice way. I don't know much number theory. I think moduler arithmetic might help. But I don't know that properly either. Can some one please help me out?






abstract-algebra number-theory chinese-remainder-theorem




abstract-algebra number-theory chinese-remainder-theorem






share|cite|improve this question















share|cite|improve this question













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edited 32 mins ago

























asked 22 hours ago









Mathisfun

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  • math.stackexchange.com/questions/288965/…
    – lab bhattacharjee
    22 hours ago


















  • math.stackexchange.com/questions/288965/…
    – lab bhattacharjee
    22 hours ago
















math.stackexchange.com/questions/288965/…
– lab bhattacharjee
22 hours ago




math.stackexchange.com/questions/288965/…
– lab bhattacharjee
22 hours ago















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