Euler商中的p次方幂
发布时间：2018-12-11 05:39
【摘要】：对于正整数n,设φ(n)和ω(n)分别是n的Euler函数和n的不同素因子的个数.对于适合a1以及gcd(a,n)=1的正整数a,形如(aφ(n)-1)/n的正整数称为Euler商.设p是奇素数,根据高次Diophantine方程的性质讨论了Euler商中p次方幂.证明了:当ω(n)≥3时,Euler商都不是p次方幂.
[Abstract]:For a positive integer n, let 蠁 (n) and 蠅 (n) be the Euler functions of n and the number of different prime factors of n, respectively. For a positive integer a suitable for a 1 and gcd (An) = 1, a positive integer in the form of (a 蠁 (n) -1) / n is called Euler quotient. Let p be an odd prime. According to the properties of higher order Diophantine equation, the power of p in Euler quotient is discussed. It is proved that when 蠅 (n) 鈮，
本文编号：2371984
[Abstract]:For a positive integer n, let 蠁 (n) and 蠅 (n) be the Euler functions of n and the number of different prime factors of n, respectively. For a positive integer a suitable for a 1 and gcd (An) = 1, a positive integer in the form of (a 蠁 (n) -1) / n is called Euler quotient. Let p be an odd prime. According to the properties of higher order Diophantine equation, the power of p in Euler quotient is discussed. It is proved that when 蠅 (n) 鈮，
本文编号：2371984
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