摘要
运用连分数理论证明了下面两个结果:①如果α,β为正实数且α不为整数,对所有正整数n满足{αn}≤{βn},那么{α}={β};②如果,αβ为正有理数,对所有素数p有{αp}≤{βp},那么{α}={β}.同时提出两个问题:①是否对n2也成立?②是否对,αβ为正无理数也成立?
In this paper, the author proves the following results： ①Let α, β be two positive real numbers and a be not integer. If {αn}≤ {βn} holds for all positive integers n, then {α}= {β}. ② Let α, β be two positive rational numbers. If {αp}≤ {βp} holds for all primes p, then{α}= {β}. Two problems are also posed. Does {αn^2}≤ {βn^2} for all n^2 imply {α}= {β} ？ Let α, β be two irrational numbers. Does {αp}≤ {βp} for all primes p imply {α}={β}？
出处
《扬州大学学报（自然科学版）》
CAS
CSCD
2006年第2期4-5,共2页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(10471064)
