数学的实践与认识
數學的實踐與認識
수학적실천여인식
MATHEMATICS IN PRACTICE AND THEORY
2009年
17期
138-143
,共6页
李用江%李昌利%李司东%葛建华
李用江%李昌利%李司東%葛建華
리용강%리창리%리사동%갈건화
Fibonacci数列%Fibonacci模数列%周期性%Fibonacci矩阵
Fibonacci數列%Fibonacci模數列%週期性%Fibonacci矩陣
Fibonacci수렬%Fibonacci모수렬%주기성%Fibonacci구진
fibonacci series%fibonacci mode series%periodicity%fibonacci mode matrix
对任意素数pr正整数r,Fibonacci数列{F_n}对pr取模构成一个数列{a_n}.若{F_n)的最小正周期为T,则{a_n}的最小正周期为p~(r-1)T,首次提出该定理,并用数学归纳法进行了证明.此外对任意正整数m,不加证明地给出了{F_nmod m}的周期性定理.
對任意素數pr正整數r,Fibonacci數列{F_n}對pr取模構成一箇數列{a_n}.若{F_n)的最小正週期為T,則{a_n}的最小正週期為p~(r-1)T,首次提齣該定理,併用數學歸納法進行瞭證明.此外對任意正整數m,不加證明地給齣瞭{F_nmod m}的週期性定理.
대임의소수pr정정수r,Fibonacci수렬{F_n}대pr취모구성일개수렬{a_n}.약{F_n)적최소정주기위T,칙{a_n}적최소정주기위p~(r-1)T,수차제출해정리,병용수학귀납법진행료증명.차외대임의정정수m,불가증명지급출료{F_nmod m}적주기성정리.
For any prime number p and positive integer r, Fibonacci series {F_n} mod p~r forms another series {a_n}. If the least positive period of {F_n} is T, then the least positive period of {a_n} is p~(r-1)T, as is firstly proposed and proved in this paper by means of the mathematical induction. Moreover, for any positive integer m, it is pointed out without proving that {F_nmod m} is periodic.
