If n is anodd integer greter than 3 but not a multiple of 3 prove that `[(x+y)^n-x^n-y^n]` is divisible by `xy(x+y)(x^2+xy+y^2).`

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^(n)=x^(n)-1 is divisible by x^(3)+x^(2)+x

x^(2n-1)+y^(2n-1) is divisible by x+y

If n is an odd integer but not a multiple of 3, then prove that xy(x+y)(x^(2)+y^(2)+xy) is a factor of (x+y)^(n)-x^(n)-y^(n).

x^(3^(n))+y^(3^(n)) is divisible by x+y, if

If n in N,x^(2n-1)+y^(2n-1) is divisible by x+y if n is

Using principle of mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all nN.

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

Prove the following by the principle of mathematical induction: x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N.