- #1
IDValour
- 25
- 2
Homework Statement
Prove that ##1900^{1990} - 1## is divisible by ##1991##
Homework Equations
##x^n - 1 = (x - 1)(x^{n-1} + x^{n-2} + ... + 1)##
The Attempt at a Solution
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Quite naturally the first step I took was to attempt the factorisation and see what that got me:
##1900^{1990} - 1 = (1900 - 1)(1900^{1989} + 1900^{1988} + ... + 1)##
And from here I somewhat fail to see where to go forward.
##1899## is not divisible by ##1991## so do I need to work on the second part? If so I am having trouble seeing how to resolve it. It does seems possible to factorise the problem down to ##(19*100)^{1990} - 1## but then again this seems highly irrelevant.
Any help on this issue would be greatly appreciated.