NUMBER THEORY: Show that 8^900 - 7 is divisable by 29 Help

[tamintl]

NUMBER THEORY: Show that 8^900 - 7 is divisable by 29 ... Help

Homework Statement

^{Show that 8^900 - 7 is divisable by 29}

Homework Equations

The Attempt at a Solution

<sup>By Fermats little theorem

(8^28)^32 x 8^4 - 7
=1^32 x 8^4 - 7
=8^4 - 7
=(8^2)^2 - 7
=64^2 - 7

NB: 64 = 29x2 + 6

therefore: 64 => 6

=(6)^2 - 7
= 36-7

29=0 mod 29</sup>



Is this correct or is there a quicker way?

thanks tamintl

 

[Dick]

That is correct and it's the quickest way I can think of to show it.