丢番图方程P(x)=n!!的正整数解  

Positive integer solution of Diophantine equation P(x) =n!!

作　　者：王璞 余奇珂 程洋 杨鹏[1] WANG Pu;YU Qike;CHENG Yang;YANG Peng(School of Science,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]辽宁科技大学理学院,辽宁鞍山114051

出　　处：《高师理科学刊》2023年第2期16-19,共4页Journal of Science of Teachers＇College and University

基　　金：大学生创新创业训练计划项目。

摘　　要：利用ABC猜想证明了对于次数大于1的整系数多项式P(x),仅有有限多个整数对(x,n)使得多项式P(x)的值为某个自然数n的双阶乘.Using ABC conjecture,it was proved that for the integer coefficients polynomial P(x) with degree greater than 1,there are only finitely many pairs of positive integers(x, n) such that the value of polynomial P(x) is a double factorial of a natural number n.

关 键 词：丢番图方程 ABC猜想 双阶乘 Brocard-Ramanujan方程 

分 类 号：O156.1[理学—数学]