3. Prove the following two theorems about pairs of "twin primes," p and (Recall that "twin primes" are primes that differ by 2.) q. b. If p and q are twin primes that are both greater than 5, then the mean of p and g is not a triangular number.
3. Prove the following two theorems about pairs of "twin primes," p and (Recall that "twin primes" are primes that differ by 2.) q. b. If p and q are twin primes that are both greater than 5, then the mean of p and g is not a triangular number.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 33E: Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that...
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![3. Prove the following two theorems about pairs of "twin primes," p and q.
(Recall that "twin primes" are primes that differ by 2.)
b. If p and g are twin primes that are both greater than 5, then the
mean of p and g is not a triangular number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8fce9fb-1e03-4f65-a00c-f05c031bc9af%2F754c36ae-01d1-4f5b-829b-5c992e7685d6%2Fvfqe05_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Prove the following two theorems about pairs of "twin primes," p and q.
(Recall that "twin primes" are primes that differ by 2.)
b. If p and g are twin primes that are both greater than 5, then the
mean of p and g is not a triangular number.
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