Mathematics, 15.11.2019 01:31, christyr2002

"prove for all integers n, that $x^{3} - n$ is even. state the proof technique you have used. justify each step in your proof."

i can work it out in my head that it must be, as n cubed will be even if n is even, and odd if n is odd. an even minus an even is still an even, an odd minus an odd is an even. but i can only prove that the equation is a multiple of 3? i'm using proof by induction.

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"prove for all integers n, that [tex]x^{3} - n[/tex] is even. state the proof technique you have use...