2004 AMC 12A Problems/Problem 25
Problem
For each integer , let
denote the base-
number
. The product
can be expressed as
, where
and
are positive integers and
is as small as possible. What is the value of
?
Solution
$a_4a_5...a_{99}=\frac{(5^3-1)(6^3-1)\cdots (100^3-1)}{4*5*6*\cdots*99*(4^3-1)(5^3-1)\cdots(99^3-1)$ (Error compiling LaTeX. Unknown error_msg)
Since isn't one of the answer choices, we need to get rid of some stuff:
Since only the two goes into 98, n is at it's minimum.