12 Feb '07 02:20

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.

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

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Eastbourne- Joined
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Eastbourne12 Feb '07 13:59

if youy cant proove something, it is assumed false.*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.

not all primes are known. so there is no proof.- Joined
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12 Feb '07 14:43Let'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?- Joined
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12 Feb '07 16:001 edit

If you can't prove something, you assume nothing. Welcome to mathematics.*Originally posted by celticcountry***if youy cant proove something, it is assumed false.**

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).- Joined
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12 Feb '07 17:11

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

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).- Joined
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p^2.sin(phi)12 Feb '07 17:58

celticcountry can go suck eggs. His posts in this thread earned him the title of idiot, did you read them?*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.- Joined
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12 Feb '07 18:09

That was my first thought. On second thought I think it*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).*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.- Joined
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12 Feb '07 18:561 edit

Yes, I did, and he is cleverer than the most people of this earth.*Originally posted by XanthosNZ***celticcountry can go suck eggs. His posts in this thread earned him the title of idiot, did you read them?**

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?