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Number Theory Test
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Number Theory Test
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25 Questions

1. What is the set of all congruence classes modulo m?

2. 1 and 0 are not prime or composite (T/F)

3. Vp(n) = 0 for finitely many primes p. (T/F)

4. If a | b and b | c, then ...

5. Transitivity property of congruence

6. What is the well ordering property?

7. For primes p, q1, q2, ... , qs with s >= 1, if p | q1 x ... x qs then

8. What is the fundamental theory of algebra?

9. Every common divisor of integers a and b divides the gcd(a,b) (T/F)

10. If b is in a + mZ then

11. What does it mean if a number is algebraic?

12. Speaking in terms of p-adic valuations, m | n if and only if

13. Let a and b be integers and m be a positive integer. A and b are congruent modulo m if and only if

14. For all primes p and all positive integers k, Vp(m^k) =

15. The set of all common divisors of integers a and b is infinite. (T/F)

16. If a | b and d is an integer, then

17. Properties of gcd(a,b).... (2)

18. If d is a non-zero integer and da | db then

19. What does it mean when integers a and b are congruent modulo m?

20. If we write b = mq + r where q and r are integers and 0 <= r < m, then

21. If a does not equal 0 then a | b if and only if b/a is in..

22. For all primes p, Vp(mn) =

23. If a | b then how does |a| compare to |b|?

24. What is Euclid's Lemma for Primes?

25. If p then q or r logical equivalence

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