Divisibility of difference of powers

Prove by induction that $x^{n} - y^{n}$ is divisible by $x + y$ when $n$ is an even positive integer.

~15 minProof · checked by AImathematical inductiondivisibility

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XII. Mathematical Induction, Examples XII, No. 5

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