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MathNet 2024-part-06 — 165 problems (EN–VI) Question 59

Math Olympiad Vault · MathNet 2024-part-06 — 165 problems (EN–VI)

Question 59

It can be shown that there exists a unique polynomial $P$ in two variables such that for all positive integers $m$ and $n$,
$$
P(m, n)=\sum_{i=1}^{m} \sum_{j=1}^{n}(i+j)^{7} .
$$
Compute $P(3,-3)$.