A New Proof of Diophantine Equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) = \Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$

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Abstract

By using algebraic number theory and $p$-adic analysis method, we give a new and simple proof of Diophantine equation $\Bigg( \begin{matrix} n \\ 2  \end{matrix} \Bigg) = \Bigg( \begin{matrix} m \\ 4  \end{matrix} \Bigg)$.



Keywords:

binomial Diophantine equation fundamental unit factorization $p$-adic analysis method.
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A New Proof of Diophantine Equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) = \Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$. (2021). Communications in Mathematical Research, 25(3), 282-288. https://www.global-sci.com/index.php/cmr/article/view/8622