论文标题
具有3个成对副本零件的组成
Compositions with 3 Pairwise Coprime Parts
论文作者
论文摘要
我们可以将$ n $以3美元的$ 3 $正整数写入多少方式，哪一对共有一个共同的因素？我们以某种类别的线性双方方程的溶液数量来表达这一数量。这使我们能够证明有$$ \ prod_ {p \ mid n} \ left（1- \ frac {1} {p^2} \ right）\ prod_ {q \ nmid n} \ left（1- \ frac {3} o（n^{3/2+o（1）}）$$这样的构图，其中产品分别超过了素数，并且不划分$ n $。这加强了Bubbolini，Luca和Spiga的先前结果（Arxiv：1202.1670）
How many ways can we write $n$ as a sum of $3$ positive integers, no pair of which share a common factor? We express this quantity in terms of the number of solutions to a certain class of linear Diophantine equations. This allows us to show that there are $$ \prod_{p \mid n} \left( 1- \frac{1}{p^2} \right) \prod_{q \nmid n} \left( 1- \frac{3}{q^2} \right) \frac{n^2}{2} + O(n^{3/2+o(1)}) $$ such compositions, where the products are over primes that respectively do and don't divide $n$. This strengthens the previous result of Bubbolini, Luca, and Spiga (arXiv:1202.1670)
