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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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