2018 AIME I Problems/Problem 11
Revision as of 19:00, 7 March 2018 by Mathislife16 (talk | contribs) (→Modular Arithmetic Solution- Strange (MASS))
Find the least positive integer such that when
is written in base
, its two right-most digits in base
are
.
Solutions
Modular Arithmetic Solution- Strange (MASS)
Note that . And
. Because
,
and
.
If , one can see the sequence
so
.
Now if , it is harder. But we do observe that
, therefore
for some integer
. So our goal is to find the first number
such that
. In other words, the
coefficient must be
. It is not difficult to see that this first
, so ultimately
. Therefore,
.
The first satisfying both criteria is
.
-expiLnCalc