polynomials

Assume you know the binomial theorem
7^2008
=(6+1)^2008
=6(M)+1^2008 where M is an integer
=6M+1
therefore the remainder is 1

2008-04-15 19:38:54 補充：
another method
since 7^2007*(7-1) is a multiple of 6
remainder of 7^2008 is equal to the remainder of 7^2007
similarly, remainder of 7^2007 is equal to the remainder of 7^2006
...
similarly, remainder of 7^2 is equal to the remainder of 7
therefore the remainder of 7^2008 when it is divided by 6 is 1