中文摘要：

从数论的角度研究了Fibonacci数列{Fn}的性质，证明了任意两个Fibonacci数的最大公因数与它们序标的最大公因数之间的关系，得到了Fibonacci数为素数的必要条件；给出Fibonacci数列在正整数表示方面应用的算法和c程序，进一步加深了对Fibonacci数列的认识。

英文摘要：

In this paper, the properties of Fibonacci sequence {Fn} is investigated from the perspective of number theory,and the relation between the greatest common divisor（GCD） of Fm and Fn and the GCD of m and n is proved. Furthermore, the necessary condition for a Fibonacci number is a prime is obtained. In addition, the algorithm and C program are presented for an application of Fibonacci sequence in represen-tation of the positive integer. The results enhance our knowledge of Fibonacci sequence.