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MA233 Final Exam - Elementary Number Theory
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MCQs on Elementary Number Theory.

MA233 Final Exam - Elementary Number Theory
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25 Questions

1. What is the multiplicative inverse of
, modulo 23?
2. Which of the following numbers is algebraic and irrational?
3. You want to find the gcd of a 15-digit number and a 20-digit number. How many divisions will it take to compute the gcd using the Euclidean algorithm?
4. Which continued fraction is the only possible candidate for the square root of a prime number?
5. Which of the following is not an aspect of the RSA encryption scheme?
6. According to Mersenne, which of the following is a good candidate for a large prime number?
7. Find the greatest common divisor of -2805 and 1287.
8. What is the multiplicative inverse of
, modulo
?
9. Suppose
. Which integers
can be expressed in the form
, where
and
are integers?
10. For which of the following sequences do we not know a closed-form formula?
11. Suppose a 7-digit number has digits
(left to right). Why can we check if
is divisible by 7 by checking whether
?
12. What class of number is useful for computing perfect numbers?
13. Evaluate
.
14. Suppose
divides
, but
does not divide
. What relationship can we establish between
and
?
15. For which integer values of
does the equation
have integer solutions for
?
16. Which of the following statements about congruence is not always true?
17. What is the correct continued fraction expansion for 5/3?
18. Essentially, what property of Liouville's number makes it transcendental?
19. Which of the following number systems is not a ring?
20. Evaluate
.
21. Which of the following rings does not satisfy the zero product property?
22. Which of the following integer sequences is not guaranteed to have infinitely many primes?
23. Which of the following rings contains all algebraic roots of positive integers?
24. Which continued fraction is the only possible candidate for the cube root of a prime number?
25. Suppose
divides
and
. What can we say about
?

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