Research On The Arithmetic Properties Of Quasi-balanced Numbers

In this paper,we introduce the arithmetical properties,the peri-odicity and uniform distribution of the Fibonacci numbers and the balancing numbers mod m,and then further study the arithmetical properties of the cobalancing numbers.The main results of this paper as follows:Firstly,we give a definition of the cobalancing numbers {b_n} and the arithmetical properties of the numbers {b_n} mod p.i.e.（1）For any odd prime p,p|b_p if and only if p≡±3（mod 8）.（2）Let p be a prime greater than 13.If p ≡±1（mod 8）,then we have b_p-1 mod p is congruent to 0 and b_p congruent to 2.respectively;If p≡±3（mod 8）,then we have b_p mod p is congruent to 0 and b_p+1 congruent to 2.respectively.Secondly,we denote the minimum positive period of the cobalanc-ing numbers {b_n} mod positive integer m（>1）by t（m）.Then,（1）For any prime p,t（p）≤（p+1）.（2）If m=2^r,then t（2^r）=2^r.（3）For 0≤i≤t（m）-1,we have b_i≡b_t（m）-1-i（mod m）.Finally,for any positive integer m（>1）,we obtain that the cobal-ancing numbers {b_n)is not uniform distribution mod m.