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

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.