pratu043
Find the condition that x^n + y^n may be divisible by x + y.



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sauravshakya
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IF n is odd

pratu043
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How do you prove that?

Libniz
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sum of odd roots factor always factor out (x+y)

pratu043
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What do you mean by that?

sauravshakya
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I know how, PLZ wait sec trying to write it down

sauravshakya
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Oh got it.... let f(x)=x^n + y^n

pratu043
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ok

pratu043
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So you should use factor theorem for this?

sauravshakya
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yep

sauravshakya
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now, when f(x) is divided by (x+y) then
REMAINDER = f(y)
= (y)^n + y^n

pratu043
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ok got that.

sauravshakya
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Now, for x^n + y^n to be divisible by x + y..
remainder = 0
or, (y)^n + y^n=0

pratu043
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ok

sauravshakya
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which is only possible when n is odd

sauravshakya
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got it?

pratu043
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ok so when n is odd, (y)^n = y
so (y)^n + y^n = y + y = 0
thanks!!

sauravshakya
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oh its like this:
when n is odd, (y)^n = (y)^n
so (y)^n + y^n = (y)^n + y^n = 0