论文标题
广义的佩尔 - 弗摩特方程和帕斯卡三角
Generalized Pell-Fermat equations and Pascal triangle
论文作者
论文摘要
使用Pascal Triangle，我们对Srinivasa Ramanujan求解的所谓的链拼图进行了简单的概括。因此，我们有兴趣计算一些整数有价值分布的中位数，第一和第三四分位数，当将算术进展的部分总和（三角形数）扩展到四面体数字及以后时，自然就会产生。我们将其简化为Pell-Fermat类型的高阶方程，这些方程很少，它承认了整数解决方案，但是，遵循Ramanujan的最初想法，我们总是可以从养生意义上找到最佳近似的整数序列。在没有关于高阶佩尔 - 弗马特方程的一般理论的情况下，我们的程序非常依赖于Mathematica的正式微积分。
Using Pascal triangle, we give a simple generalization to the so-called STRAND Puzzle solved by Srinivasa Ramanujan. Thus we are interested in computing the median, first and third quartiles of some integer valued distributions, arising naturally when extending partial sums of the arithmetic progression (triangular numbers) to tetrahedral numbers and beyond. We show this reduces to equations of Pell-Fermat type of higher order, which admit very few integer solutions, but for which, following Ramanujan's original idea, we can always find integer sequences of best approximation, in the Diophantine sense. In absence of a general theory on Pell-Fermat equation of higher order, our procedure relies much on formal Calculus with Mathematica.
