I Won't Use A Calculator!
Find the remainder when is divided by 100.
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2 solutions
Moderator note:
Good approach of using the binomial theorem and realizing that .
Another way is to expand , to easily get the factor of 100.
Let 1 0 C n = C n 1 1 1 0 = ( 1 0 + 1 ) 1 0 = C 0 1 0 1 0 + C 1 1 0 9 + … + C 9 1 0 + C 1 0 ≡ C 9 1 0 + C 1 0 ≡ 1 0 1 ≡ 1 m o d 1 0 0