I am trying to prove that 3 divides [tex]n^3~-7n+3[/tex] for all integers n greater than or equal to 0.(adsbygoogle = window.adsbygoogle || []).push({});

I have gotten to this point:

[tex]3|(k~+~1)^3~-~7(k~+~1)~+~3[/tex]

Where I try to show that is true for k+1. I have been scribbling on scrap paper trying to figure it out. I've expanded the expression countless times no avail.

Could someone give me a hint?

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# New to induction, stuck on a proof and i need some help

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