97年 - 97 淡江大學轉學考離散數學#55809

科目：轉學考-離散數學 | 年份：97年 | 選擇題數：0 | 申論題數：5

試卷資訊

所屬科目：轉學考-離散數學

選擇題 (0)

申論題 (5)

1. Prove that if an integer a is such that a — 2 is divisible by 3, then α²- 1 is divisible by 3. (20%)

【已刪除】2. Determine Ihe number of (staircase) paths in the xy plane from (2, 1) to (7，4), as shown in the following figure, where each such path is made up of individual steps going one unit to the right (R) or one unit upward (U). (20%)

【已刪除】3. Prove by induction lhat for any

. (20%)

【已刪除】4. Solve the recurrence relation

(20%)

5. Prove or disprove that any subset of size six from the set S= {1, 2, 3,..., 9} must contain two elements whose sum is 10. (20%)