论文标题
Mobius功能和一致数字
The Mobius Function and Congruent Numbers
论文作者
论文摘要
这项工作提供了毕达哥拉斯三元组的一致数字的完整表征。具体而言，我们表明每个一致的数字都可以写成$ \ frac {nm \ left（m-n \ right）\ left（m+n \ right）} {σ^2} $$如$ qutt（m-n \ weft（m-n \ right）\ weft（m+weft（m+prig）， \缩号σ\vertρ（nm）$$为$ρ（α）$表示其参数的非平方自由部分$α$。因此，为了找到一致的数字，就足以设计条件，以便相等的$μ（m-n）+1 = \ gcd（m，n）$或$μ（m+n）+1 = \ gcd（m，n）$ holds，$ $ $ $ $ $ $ $ $是莫比乌斯的功能。
This work provides a complete characterization of congruent numbers in terms of Pythagorean triples. Specifically, we show that every congruent number can be written as $$\frac{nm\left(m-n\right)\left(m+n\right)}{σ^2}$$ were as $$σ\vert ρ\biggl(\left(m-n\right)\left(m+n\right)\biggr),\indent \text{or} \indent σ\vert ρ( nm )$$ were $ρ(α)$ denotes the non-square free part of its argument $α$. As a consequence, in order to find congruent numbers it suffices to devise a condition so that the equality $μ(m-n)+1 = \gcd(m,n)$ or $μ(m+n)+1 =\gcd(m,n)$ holds, were $μ$ is the Mobius function.
