You are Here: Home >< Maths

# Linear Algebra Proof watch

1. Prove that there exist infinitely many primes p such that p=3 mod 4.
2. (Original post by DB9)
Prove that there exist infinitely many primes p such that p=3 mod 4.
first note if p1=4k+1 p2=4m+1 then p1p2 is of form 4n+1

Assume p1,....pn are all the primes of the form 4k+3
let P=p1p2....pn and consider the number
N=4P+3
since this is of the form 4P+3 by using the first observation (ie product of primes of form 4k+1 gives a number of that form) N must have a prime factor of the form 4k+3 for some k.
But this prime factor can not be one the primes in our assumption since we would have a remainder of 3

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 10, 2006
Today on TSR

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams