所屬科目： 中山◆資工◆離散數學
1. Let x1, x2, , be a sequence of n integers. A consecutive subsequence of x1,x2,... ., is a subsequence for some i, j, 1 ≤ i ≤ j ≤n. Show that for any k, I k n, there is a consecutive subsequence whose sum is divisible by k.
2. Assume that a sequence of numbers is deined by x0 = 0, x1 = 1, and = ＞ 1. Find generating function for the sequence, and then find an explicit expression for un.
3. Show that Give combinatorial explanation to the equation.
6. Fibonacci numbers are deined as f0 = 0, f1= 1 and for n ＞.1. Show that is even, for every positive integer k. .
(a) Show that if'n is prime, then n divides for every i, 1 ≤i＜n.
(b) Show that if n is composite, then n does not divide for some i, 1 ≤i ＜n.
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be a sequence of n integers. A consecutive subsequence of x1,x2,... ., 
is a subsequence
for some i, j, 1 ≤ i ≤ j ≤n. Show that for any k, I k n, there is a consecutive subsequence whose sum is divisible by k.
= 
＞ 1. Find generating function for the sequence, and then find an explicit expression for un.
Give combinatorial explanation to the equation.
for n ＞.1. Show that 
is even, for every positive integer k. .
for every i, 1 ≤i＜n.
for some i, 1 ≤i ＜n.