【摘要】：對(duì)于正整數(shù)n,設(shè)φ(n)和ω(n)分別是n的Euler函數(shù)和n的不同素因子的個(gè)數(shù).對(duì)于適合a1以及gcd(a,n)=1的正整數(shù)a,形如(aφ(n)-1)/n的正整數(shù)稱(chēng)為Euler商.設(shè)p是奇素?cái)?shù),根據(jù)高次Diophantine方程的性質(zhì)討論了Euler商中p次方冪.證明了:當(dāng)ω(n)≥3時(shí),Euler商都不是p次方冪.
[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，

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