wsldam said:
tiny-tim said:hi wsldam! welcome to pf!
isn't that another way of saying that 2m can never be of the form 3n + 1 ?
The expression "3^n+1" refers to a mathematical sequence in which n is a positive integer. This sequence is often studied in number theory and has connections to prime numbers.
Having an odd prime divisor in the expression "3^n+1" is significant because it helps to reveal patterns and properties of the sequence. It also has implications for understanding the distribution of prime numbers.
Yes, for n=2, the expression "3^n+1" becomes "3^2+1=10". This has an odd prime divisor of 5.
There is no general formula for determining when "3^n+1" has an odd prime divisor. However, there are certain patterns and criteria that have been identified by mathematicians, such as the Lucas-Lehmer test, which can be used to determine if a specific value of n will result in an odd prime divisor.
Studying "3^n+1" and its odd prime divisors can have various implications in number theory and other branches of mathematics. It has been used in the study of Mersenne primes, which are prime numbers of the form "2^n-1". It also has connections to the Collatz conjecture, a famous unsolved problem in mathematics. Additionally, understanding the distribution of prime numbers can have practical applications in cryptography and computer science.