Proof. Consider any number n. Let n! be the factorial of n, and consider the number...
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Proof. Consider any number n. Let n! be the factorial of n, and consider the number p = n! + 1. So p is larger than n, and it has a remainder of 1 when divided by any number up to n. So p is prime, and we have therefore found a prime number above n. So there are infinitely many prime numbers. Proof. Consider any number n. Let n! be the factorial of n, and consider the number p = n! + 1. So p is larger than n, and it has a remainder of 1 when divided by any number up to n. So p is prime, and we have therefore found a prime number above n. So there are infinitely many prime numbers.
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This is a proof by contradiction of Euclids theorem which states that there are infinitely many ... View the full answer
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Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
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