Mock AIME 5 Pre 2005 Problems/Problem 12

Problem

Let . Find the sum of the digits of .

Solution

By the binomial theorem,

\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} (Error compiling LaTeX. Unknown error_msg)

and so the sum of the digits is

See also

Mock AIME 5 Pre 2005 (Problems, Source)
Preceded by Problem 11	Followed by Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15