2024 AMC 8 Problems/Problem 4
Problem
When Yunji added all the integers from to
, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
Solution 1
The sum of the numbers from to
is
Denote the number left out when adding to be
. Thus,
is a perfect square. We could rigorously solve the values of
such that
is a perfect square. We also know that
must be between
and
inclusive, so the answer is
.
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