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## Homework Statement

I am to prove that [tex]3^{6n}-2^{6n}[/tex] is divisible by 35 for all n[tex]n\in\aleph[/tex] using induction.

## Homework Equations

[tex]3^{6n}-2^{6n}=35x[/tex] where [tex]x\in\aleph[/tex] for all [tex]n\in\aleph[/tex] and

## The Attempt at a Solution

Base:

[tex]3^{6(1)}-2^{6(1)}=35*x[/tex]

[tex]665=35x[/tex]

x=19

thus since 19 is an element of natural numbers the base case is true

Then I make this assumption

Assume:

[tex]3^{6k}-2^{6k}=35x[/tex]

Inductive step:

[tex]3^{6(k+1)}-2^{6(k+1)}=35x[/tex]

[tex]3^{6}3^{6k}-2^{6}2^{6k}=35x[/tex]

and i don't know where to go from here, i've tried lots of things, but i cant reduce it down to the assumption