My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree2Thanks
  • 2 Post By cjem
Reply
 
LinkBack Thread Tools Display Modes
February 23rd, 2019, 09:07 AM   #1
Senior Member
 
Joined: Jan 2016
From: Blackpool

Posts: 104
Thanks: 2

number congruent to -1mod 3

Show that if N is congruent to -1mod3 then there exists at least one prime factor congruent to -1mod3. Hence show there are infinitely many primes of the form 6n-1.
Jaket1 is offline  
 
February 23rd, 2019, 01:16 PM   #2
Senior Member
 
Joined: Aug 2017
From: United Kingdom

Posts: 313
Thanks: 112

Math Focus: Number Theory, Algebraic Geometry
As N is -1 mod 3, each of N's prime factors must be 1 or -1 mod 3. If they were all 1 mod 3, then their product (which is N) would be 1 mod 3, which is a contradiction. So at least one of them is -1 mod 3.

For the second part, consider the usual proof that there are infinitely many primes and see if you can apply the above result.
Thanks from topsquark and Jaket1
cjem is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
1mod, congruent, number



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
h^2 congruent to h mod n claudiohorvi Number Theory 5 November 25th, 2013 07:15 AM
Are they congruent at 0 mod y? coffee_leaf Number Theory 1 September 2nd, 2012 10:07 PM
((my) mod n ) congruent to n-1 smslca Number Theory 4 January 28th, 2012 11:21 PM
need help for a proof about congruent, and gcd kenhct Abstract Algebra 1 November 2nd, 2010 12:38 PM
x^2 congruent to 2 mod 5 sea_wave Number Theory 4 February 11th, 2010 12:16 AM





Copyright © 2019 My Math Forum. All rights reserved.