Yet another number problem

True or false:

if a, b, c and d are positive integers, and ab=cd, then a+b+c+d cannot be a prime number.

Originally posted by David113
True or false:

if a, b, c and d are positive integers, and ab=cd, then a+b+c+d cannot be a prime number.

unproveable.

so false.

Originally posted by celticcountry
unproveable.

so false.

If you wish to state that it is unprovable you need to prove that this is the case.
And even if it is unprovable that doesn't mean it's false unless a counter example exists.

Originally posted by XanthosNZ
If you wish to state that it is unprovable you need to prove that this is the case.
And even if it is unprovable that doesn't mean it's false unless a counter example exists.

if youy cant proove something, it is assumed false.

not all primes are known. so there is no proof.

Originally posted by celticcountry
if youy cant proove something, it is assumed false.

not all primes are known. so there is no proof.

You're an idiot.

Let's try this:
If ab=cd, then there exist integers x,y, z and t such that:
a=xz, b=yt, c=xt, d=yz. (one or more of these integers may be equal to 1).
Then a+b+c+d = xz+yt+xt+yz = x(z+t) + y(z+t) = (x+y)(z+t) which consists of two different integers, hence can never be a prime. Does that sound right?

Originally posted by celticcountry
if youy cant proove something, it is assumed false.

If you can't prove something, you assume nothing. Welcome to mathematics.

There are a few conjectures out there that people think are probably true, but we can't prove. Fermat's Last Theorem used to be an example.


(Even if you can prove it's unproveable, you're still on shaky ground assuming it's false).

Originally posted by XanthosNZ
You're an idiot.

agreed

Originally posted by ilywrin
Let's try this:
If ab=cd, then there exist integers x,y, z and t such that:
a=xz, b=yt, c=xt, d=yz. (one or more of these integers may be equal to 1).
Then a+b+c+d = xz+yt+xt+yz = x(z+t) + y(z+t) = (x+y)(z+t) which consists of two different integers, hence can never be a prime. Does that sound right?

Maybe I'm being stupid, but why is this true?

If ab=cd, then there exist integers x,y, z and t such that:
a=xz, b=yt, c=xt, d=yz. (one or more of these integers may be equal to 1).

Originally posted by XanthosNZ
You're an idiot.

Showing once more your complete lack of social competence...

Originally posted by FabianFnas
Showing once more your complete lack of social competence...

You are also an idiot.

Originally posted by XanthosNZ
You are also an idiot.

And you are the only one in the whole world who is not an idiot?
How lonely you must feel...

I don't mind you calling me an idiot, I know you too good for that.
But an apology to celticcountry would be appropriate.

Originally posted by FabianFnas
And you are the only one in the whole world who is not an idiot?
How lonely you must feel...

I don't mind you calling me an idiot, I know you too good for that.
But an apology to celticcountry would be appropriate.

celticcountry can go suck eggs. His posts in this thread earned him the title of idiot, did you read them?

Originally posted by Fat Lady
Maybe I'm being stupid, but why is this true?

If ab=cd, then there exist integers x,y, z and t such that:
a=xz, b=yt, c=xt, d=yz. (one or more of these integers may be equal to 1).

That was my first thought. On second thought I think it is true, but it isn't obvious.

If you define x as the product of the prime factors of a that it shared with c, and y as the product of the prime factors of b that it shares with d...

...and then you can define z and t by a = xz and b = yt...

...then I think that you can show that c = xt and d = yz. But I haven't worked it through fully yet.

Originally posted by XanthosNZ
celticcountry can go suck eggs. His posts in this thread earned him the title of idiot, did you read them?

Yes, I did, and he is cleverer than the most people of this earth.

You didn't like when I call you social incompetent, do you think he likes to be called an idiot? This is the flaw in your personality that I call lack of emotional competence.

Now you force me to show for everybody your lack of social competence and lack of emotional competence.

How does it feel to be without both social and emotional competence?

Now, now, just say "I apologize, I was stupid to say that" to celticcountry? Just to show that I am wrong in the personality analyze of you?