Number Theory Test 2
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Avg score: 33% • Most missed: “If d is an integer and p !| d then ((ad^2)/p)...”
Number Theory Test 2
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25 Questions

1. What are the properties of a group? (3)

2. What is a field?

3. a is congruent to b (mod m) if and only if...

4. The set (Z/mZ)^X is a group and a ring (T/F)

5. If gamma is a primitive root modulo the odd prime p, then... gamma^(p-1)/2 =

6. Let alpha = a+mZ be a unit. If alpha is a primitive root modulo m, then ....

7. If d is an integer and p !| d then ((ad^2)/p)...

8. Let f(X) be in Z[X]. We define f(alpha = a+mZ)

9. If every non-zero element in Z/mZ has a multiplicative inverse then Z/mZ is a ________

10. Euler Phi Function

11. The congruence aX congruent to b (mod m) has a solution if and only if ...

12. What is a quadratic residue or square modulo p?

13. Fermat's little theorem

14. For integers with gcd(m,n) = 1, phi(mn) =

15. What is a primitive root modulo m?

16. Wilson's Theorem

17. A polynomial X^2+bX+c has roots in Z/pZ if and only if its discriminant is a square modulo p (T/F)

18. Quadratic Formula Proposition (2)

19. If a is congruent to b (mod p) then (a/p)...

20. If p is prime then the group of units of Z/pZ consists of...what is the size of this group of units?

21. A congruence of integers is equivalent to an equality of congruence classes (T/F)

22. How many elements are in the congruence class Z/mZ?

23. What is the Legendre Symbol (a/p)?

24. Z/mZ is not a ring (T/F)

25. How do the rings Z/mZ and Z differ? (3)

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