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Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O There are infinitely many prime numbers. O Any strictly decreasing sequence of nonnegative integers must terminate. O If a product of two integers is divisible by a prime numbers, then one of these two integres must be divisible by a prime number. O The GCD of two numbers does not change if we subtract a multiple of one of the numbers from the other number. O If a, b are two positive integers, then we can always divide one by the other one with a remainder.

Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O There are infinitely many prime numbers. O Any strictly decreasing sequence of nonnegative integers must terminate. O If a product of two integers is divisible by a prime numbers, then one of these two integres must be divisible by a prime number. O The GCD of two numbers does not change if we subtract a multiple of one of the numbers from the other number. O If a, b are two positive integers, then we can always divide one by the other one with a remainder.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 34E
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Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O There are infinitely many prime numbers. O Any strictly decreasing sequence of nonnegative integers must terminate. O If a product of two integers is divisible by a prime numbers, then one of these two integres must be divisible by a prime number. O The GCD of two numbers does not change if we subtract a multiple of one of the numbers from the other number. O If a, b are two positive integers, then we can always divide one by the other one with a remainder.
Transcribed Image Text:Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O There are infinitely many prime numbers. O Any strictly decreasing sequence of nonnegative integers must terminate. O If a product of two integers is divisible by a prime numbers, then one of these two integres must be divisible by a prime number. O The GCD of two numbers does not change if we subtract a multiple of one of the numbers from the other number. O If a, b are two positive integers, then we can always divide one by the other one with a remainder.
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