2021 JMPSC Accuracy Problems/Problem 15
Revision as of 12:34, 11 July 2021 by Geometry285 (talk | contribs)
Problem
For all positive integers define the function
to output
For example,
,
, and
Find the last three digits of
Solution
Notice that ,
,
, and
ends in
for all
. So, the last 3 digits of
are the last
digits of
, which are
.
~Mathdreams
Solution 2 (More Algebraic)
We only care about the last
digits, so we evaluate
. Note the expression is simply
, so factoring a
we have
. Now, we can divide by
to get
Evaluate the last
digits to get
~Geometry285