10 questions in an introductory number theory course for undergraduates.

 

 

Number Theory
Quiz 2 1) From the sieve of Eratosthenes we can see that π(20) is
A: 14
B: 19
C: 8
D: 2
2) If a and b are relatively prime positive integers, then the arithmetic
progression an + b; n = 1, 2, 3, ... contains
A: No primes
B: Infinitely many primes
C: An odd number of primes
D: A finite number of primes
3) For any positive integer n there are at least
A: n primes less than n
B: No primes greater than n2
C: n consecutive composite positive integers
D: None of the above
4) The Greatest Common Divisor between 200 and 350 is:
A: 25
B: 20
C: 350
D: 50
5) The Greatest Common Divisor between 19 and 17 is:
A: 19
B: 17
C: 1
D: None of the above 1 6) Every prime number is an odd positive integer.
True
False
7) There are infinitely many prime numbers.
True
False
8) π(n)
n
log n tends to 1 as n tends to infinity True
False
9) The greatest common divisor of the integers a and b, not both 0, is the
greatest positive integer that is a linear combination of a and b.
True
False
10) There is a formula that only generates primes.
Hint: A formula is not necessarily a simple function such as y = 3x + 8. A
formula can be recursive, multi-variable, or both.
True
False 2

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• 1492943618-Quiz 2.pdf