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6. A classic unsolved problem in number theory asks if there are infinitely many pairs of "twin primes", pairs of primes separated by 2, such as 3 and 5, 11 and 13, or 71 and 73. Prove that the only prime triple (i.e. three primes, each 2 from the next) is 3, 5, 7. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 7. Prove that for any natural number 1, 2+2² +2³+...+2=2+1-2 Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.

6. A classic unsolved problem in number theory asks if there are infinitely many pairs of "twin primes", pairs of primes separated by 2, such as 3 and 5, 11 and 13, or 71 and 73. Prove that the only prime triple (i.e. three primes, each 2 from the next) is 3, 5, 7. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 7. Prove that for any natural number 1, 2+2² +2³+...+2=2+1-2 Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.8: Adding And Subtracting Radicals
Problem 5E
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6. A classic unsolved problem in number theory asks if there are infinitely many pairs of "twin primes", pairs of primes separated by 2, such as 3 and 5, 11 and 13, or 71 and 73. Prove that the only prime triple (i.e. three primes, each 2 from the next) is 3, 5, 7. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 7. Prove that for any natural number 1, 2+2² +2³. + +2n = 2n+1-2 Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
Transcribed Image Text:6. A classic unsolved problem in number theory asks if there are infinitely many pairs of "twin primes", pairs of primes separated by 2, such as 3 and 5, 11 and 13, or 71 and 73. Prove that the only prime triple (i.e. three primes, each 2 from the next) is 3, 5, 7. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 7. Prove that for any natural number 1, 2+2² +2³. + +2n = 2n+1-2 Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
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