TU Wien:Discrete Mathematics VO (Gittenberger)/Written Exam 2024-07-02
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- Is the polynomial p(x) = x^6 + x^5 + x^2 + x + 1 primitive in Z_2?
- Compute the number of integers x with 1 <= x <= 1000000 where x is neither a square nor a 3rd, 4th, or 5th power of some positive integer y.
- For any simple, undirected graph G, prove via induction over α0(G), that the following holds χ(G) ≤ 1 + maxv in V d(v). χ(G) is the chromatic value of the graph.
- Use the Chinese remainder theorem to solve the following system of congruence relations: 3x = 12 mod 13, 5x = 7 mod 22, 2x = 3 mod 7