【摘要】 考虑差分方程xn+1=a+b0xn+b1xn-1+…+bk-1xn-(k-1)xn-k其中a,bi是非负实数,a+∑k-1i=0bi>0,k∈{1,2,…}.证明了当k+1为素数时,方程的任半环不超过(2k+2)项;当k+1为合数且只有一个bi≠0时,方程的任半环不超过2k+1+km+0 1项,其中m0=min{m m为k+1的大于1的因数}.结果部分回答了C.Darwen and W.T.Patula提出的公开问题.更多还原

【Abstract】 In this paper,we study further on the cycle length for the difference equationx_n+1=(a+∑k-1[]i=0b_ix_n-i)[]x_n-kwhere a and b_i are nonnegative numbers and（a+∑k-1[]i=0b_i）>0.It is showed that if k+1 is a prime number,then every semicycle has no more than（2k+2） terms;if k+1 is a composite number and only one b_i≠0,then every semicycle has no more than 2k+1+k+1[]m₀.where m₀=min{m|m>1,is a factor of k+1}.This result partially answer the open question posed by C.Darwen and W.T.Patula.更多还原