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did U silly this?

Source: 2023 AIME I #10

February 8, 2023
AMCAIMEAIME I

Problem Statement

There exists a unique positive integer aa for which the sum U=∑n=12023⌊n2−na5⌋U=\sum_{n=1}^{2023}\left\lfloor\dfrac{n^{2}-na}{5}\right\rfloor is an integer strictly between −1000-1000 and 10001000. For that unique aa, find a+Ua+U.
(Note that ⌊x⌋\lfloor x\rfloor denotes the greatest integer that is less than or equal to xx.)
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