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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**