Find the condition that x n - y n may be divisible by x+y?
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The shortest possible way could be following ―
Assumption: n is any integer.
For x^n-y^n to be divisible by x+y, the remainder on division should be 0 (zero).
For this,
x+y=0 gives,
x=-y
On substitution in given expression,
(-y)^n-y^n=0 [For divisibility]
=> (-y)^n = y^n
This is possible only when n is an even integer.
[If you find this helpful, please mark the answer thank you and comment/message for further queries.]
Assumption: n is any integer.
For x^n-y^n to be divisible by x+y, the remainder on division should be 0 (zero).
For this,
x+y=0 gives,
x=-y
On substitution in given expression,
(-y)^n-y^n=0 [For divisibility]
=> (-y)^n = y^n
This is possible only when n is an even integer.
[If you find this helpful, please mark the answer thank you and comment/message for further queries.]
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