Divisibility Induction (1 Viewer)

[SuxMATH]

Prove for n>0, 7^n +3n(7^n) - 1 is a multiple of 9

 

[jordankime]

Okay, so this was actually quite a tricky question, although definitely something that could come up in an exam. The all important line to watch out for is 28.7^k + 84k.7^k - 63k.7^k - 28 + 27, as this enables you to take out a common factor of 28 from 3 of the terms, substitute in and then take out a common factor of 9 of everything.

Hope that helps.