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Which polynomial represents the numbers in the array?

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April 19, 2013
algebrapolynomialanalytic geometry

Problem Statement

The squares of a squared paper are enumerated as shown on the picture. ⋱10⋱69⋱35812⋱124711⋱\begin{array}{|c|c|c|c|c|c} \ddots &&&&&\\ \hline 10&\ddots&&&&\\ \hline 6&9&\ddots&&&\\ \hline 3&5&8&12&\ddots&\\ \hline 1&2&4&7&11&\ddots\\ \hline \end{array} Devise a polynomial p(m,n)p(m, n) in two variables such that for any m,n∈Nm, n \in \mathbb{N} the number written in the square with coordinates (m,n)(m, n) is equal to p(m,n)p(m, n).
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