Question

1. (10 points) Prove the following statements by contradiction: (a) If the sum of two primes is prime, then one of the primes must be 2. (b) There are infinitely many primes. (This is a famous result in the history of mathematics.)

          1. (10 points) Prove the following statements by contradiction:
(a) If the sum of two primes is prime, then one of the primes must be 2.
(b) There are infinitely many primes. (This is a famous result in the history of mathematics.)

1. (10 points) Prove the following statements by contradiction:
(a) If the sum of two primes is prime, then one of the primes must be 2.
(b) There are infinitely many primes. (This is a famous result in the history of mathematics.)

Added by John P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

03/15/2023

Step 1

So, we have: $p + q = r$ Now, let's assume that neither p nor q is equal to 2. Since p and q are both prime numbers greater than 2, they must be odd numbers. Let's represent p and q as: $p = 2m + 1$ $q = 2n + 1$ where m and n are integers. Now, let's add p Show more…

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(10 points) Prove the following statements by contradiction: (a) If the sum of two primes is prime, then one of the primes must be 2. (b) There are infinitely many primes. (This is a famous result in the history of mathematics.)