2002 AMC 12P Problems/Problem 13
Problem
What is the maximum value of for which there is a set of distinct positive integers
for which
Solution
Note that
When ,
.
When ,
.
Therefore, we know .
Now we must show that works. We replace one of
with an integer
to account for the amount under
, which is
.
Essentially, this boils down to writing as a difference of squares. We know
, so we assume there exist positive integers
and
where
and
such that
.
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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All AMC 12 Problems and Solutions |
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