2011 AIME I Problems/Problem 11
Problem
Let be the set of all possible remainders when a number of the form
,
a nonnegative integer, is divided by
. Let
be the sum of the elements in
. Find the remainder when
is divided by
.
Solution
Note that the cycle of remainders of will start after
because remainders of
will not be possible after (the numbers following will always be congruent to 0 modulo 8). Now we have to find the order. Note that
. The order is
starting with remainder
. All that is left is find
in mod
after some computation.
See also
2011 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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