- 1.
Let m ∈ Z+ with m odd. Prove that there exists a positive integer n such that m divides 2n − 1.
- 題型：問答題
- 難易度：尚未記錄
- 2.
Determine the number of integer solutions to x1 + x2 + x3 + x4 = 19 where −5 ≤ xi ≤ 10 for all 1 ≤ i ≤ 4.
- 題型：問答題
- 難易度：尚未記錄
- 3.
If a fair die is rolled 12 times, what is the probability that the sum of the rolls is 30?
- 題型：問答題
- 難易度：尚未記錄
- 4.
For Σ = {0, 1, 2, 3}. For n ≥ 1, let an count the number of strings in Σn containing an odd number of 1's. Find and solve a recurrence relation for an.
- 題型：問答題
- 難易度：尚未記錄
- 5.
Prove that every loop-free connected planar graph has a vertex v with deg(v) < 6.
- 題型：問答題
- 難易度：尚未記錄