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tamintl
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NUMBER THEORY: Show that 8^900 - 7 is divisable by 29 ... Help
Show that 8^900 - 7 is divisable by 29
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
Is this correct or is there a quicker way?
thanks tamintl
Homework Statement
Show that 8^900 - 7 is divisable by 29
Homework Equations
The Attempt at a Solution
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
Is this correct or is there a quicker way?
thanks tamintl