You are Here: Home >< Maths

# Simple Proof Watch

1. I'm asked to prove that:

For any natural numbers a, b, c with c greater than or equal to 2, there is a natural number n such that an^2 + bn + c is not a prime.

I feel like my approach should be to let x be non-prime such that an^2 + bn + c = x. Then to show there is a solution n, in the natural numbers to an^2 + bn + (c - x) = 0, whilst somehow making use of the fact x can be wrote as the product of prime factors? Not sure where to get stuck in though..
2. Seems like quite a tricky gcse question
3. (Original post by marcus2001)

For any natural numbers a, b, c with c greater than or equal to 2, there is a natural number n such that an^2 + bn + c is not a prime.

I feel like my approach should be to let x be non-prime such that an^2 + bn + c = x. Then to show there is a solution n, in the natural numbers to an^2 + bn + (c - x) = 0, whilst somehow making use of the fact x can be wrote as the product of prime factors? Not sure where to get stuck in though..
hey you can solve this by proof by contradiction. best thing to assume is that there are natural numbers , a, b ,c greater and equal to 2 , such that an^2 + bn + c is a prime.

However if we take a=b=c=2 we have , 2n^2+2n+2=2(n^2+n+1) which is a contradiction ( as 2 being factor means it not a prime, remember a prime only has factor 1 and the number itself). hence we have proved your result

NB:a for stuff like this do proof by contraction - assume the thing is true and give a counterexample. Hence the opposite must hold
4. Proof by contradiction would be a good way to do this, suppose that there does not exist a natural number such that is not a prime. Then, only and divides

However, since the number so it would be enough to show that there exists an such that divides - which is a contradiction.
5. (Original post by Namige)
Seems like quite a tricky gcse question
Then why don't you help instead of uselessly posting that?
6. (Original post by Noble.)
Proof by contradiction would be a good way to do this, suppose that there does not exist a natural number such that is not a prime. Then, only and divides

However, since the number so it would be enough to show that there exists an such that divides - which is a contradiction.
how would i find the n? i swear we use a.b.c for this?
7. ermm am i being a bit thick ? all you have to do is let n = c
8. (Original post by the bear)
ermm am i being a bit thick ? all you have to do is let n = c
LOL you're right! It should've been obvious from the fact but typically I overcomplicated it.
9. (Original post by falcon pluse)
how would i find the n? i swear we use a.b.c for this?
Look at what 'the bear' posted, that's one way to answer this question in one line
10. Just proceed by noting that if we take n=c then,

an^2 + bn + c = c(ac+b+1)

which is clearly not prime since divisible by c.
11. (Original post by Rooinek)
Just proceed by noting that if we take n=c then,

an^2 + bn + c = c(ac+b+1)

which is clearly not prime since divisible by c.
Someone has already pointed this out, there's no need to bump a 9 hour old thread if you're just going to repeat what has already been said.

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: March 31, 2013
Today on TSR

### What is the latest you've left an assignment

And actually passed?

### Simply having a wonderful Christmas time...

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.