Problem 1:
Let $S=1^1+2^2+3^3+ ... +2010^{2010}$ . What is the remainder when $S$ is divided by $2$?
BdMO National Higher Secondary 2010/1
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Re: BdMO National Higher Secondary 2010/1
n^n is even if n is even or odd if n is odd.Now u get the result 1
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Re: BdMO National Higher Secondary 2010/1
Same type of Problem.