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Counting Subsets and the Binomial Theorem

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The Power Set on a finite set S, denoted P(S), has 2|S| elements. Similarly enough, Sum_{i}^{n} C(n, i) = 2n...
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The Importance of Multiplicative Functions

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I came across this thread today, where the OP was attempting to solve a problem regarding counting divisors. Here, the use of a multiplicative function provided means to optimize when counting divisors for larger numbers.

First, let's define two terms- multiplicative and completely multiplicative. A multiplicative function f...

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July 2013

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