Difference between revisions of "Mock AIME 5 Pre 2005 Problems/Problem 12"
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== Solution == | == Solution == | ||
− | By the [[binomial theorem]], < | + | By the [[binomial theorem]], <math>\begin{aligned} 101^4 + 256 &= (100 + 1)^4 + 256 \\ &= (100^4 + 4\cdot 100^3 + 6 \cdot 100^2 + 4 \cdot 100 + 1) + 256 \\ &= 104060401 + 256 = 104060657, \end{aligned}</math><math> and so the sum of the digits is </math>1+4+6+6+5+7 = \boxed{29}.$ |
== See also == | == See also == |