Hint
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Answer
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Term for a number that has no positive divisors other than 1 and itself Ex: 2, 3, 5, 7, 11, 13, etc.
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Prime
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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.
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Composite
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The greatest number that divides both of a pair of two numbers
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Greatest common divisor
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The smallest number that is a multiple of both of a pair of two numbers
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Least common multiple
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Name of the theorem that states that a number can be written uniquely as a product of powers of primes, known as prime factorization?
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Fundamental Theorem of Arithmetic
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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.
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Dirichlet's Theorem
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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)?
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Prime Number Theorem
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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?
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Exactly divides
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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?
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Powerful
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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?
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Division Algorithm
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What is the algorithm we use to find the greatest common factor of two numbers?
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Euclidean Algorithm
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What is the term for methods that eliminate composite numbers from a list of integers, leaving only prime numbers remaining?
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Sieve
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What Greek mathematician pioneered the above methods?
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Eratosthenes
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What is the term for primes of the form (2^n) - 1, where n is a positive integer? Examples: 3, 7, 31, etc.
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Mersenne primes
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What is the term for primes of the form (2^(2^n)) + 1, where n is a nonnegative integer? Examples: 3, 5, 17, etc.
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Fermat primes
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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?
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Goldbach conjecture
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