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Number Theory Terminology, Part 1 - Statistics

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  • This quiz has been taken 22 times
  • The average score is 4 of 16
Answer Stats
Hint Answer % Correct
Term for a number that has no positive divisors other than 1 and itselfEx: 2, 3, 5, 7, 11, 13, etc. Prime
100%
The greatest number that divides both of a pair of two numbers Greatest common divisor
63%
The smallest number that is a multiple of both of a pair of two numbers Least common multiple
63%
What is the term for a number that has positive divisors other than 1 and itself?Ex: 4, 6, 8, 10, 12, 14, 15, etc. Composite
42%
Given any integers a, b, we can find unique integers q, r such that 0 <= r < b, and a = bq + r. What is the name of this theorem? Division Algorithm
21%
What is the algorithm we use to find the greatest common factor of two numbers? Euclidean Algorithm
21%
Name of the theorem that states that a number can be written uniquely as a product of powers of primes, known as prime factorization? Fundamental Theorem of Arithmetic
21%
Name of the theorem that states that the number of primes less than or equal to a number X is asymptotically approaches x/ln(x)? Prime Number Theorem
21%
What Greek mathematician pioneered the above methods? Eratosthenes
16%
What is the term for primes of the form (2^(2^n)) + 1, where n is a nonnegative integer?Examples: 3, 5, 17, etc. Fermat primes
16%
What is the name of the conjecture that every even integer > 2 can be written as the sum of two (not necessarily distinct) prime numbers? Goldbach conjecture
16%
What is the term for primes of the form (2^n) - 1, where n is a positive integer?Examples: 3, 7, 31, etc. Mersenne primes
16%
What is the term for methods that eliminate composite numbers from a list of integers, leaving only prime numbers remaining? Sieve
16%
Name of the theorem that states that there are infinitely many primes of the form a + nb, where n is an integer and GCD(a, b) = 1. Dirichlet's Theorem
11%
Term for when the k-th power of a prime number, p, is the highest power of p that divides a number b, denoted by (p^k) || b? Exactly divides
0%
If we have an integer n, where all primes appearing in the prime factorization of n have an exponent of at least 2, what adjective do we give to n? Powerful
0%
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