Determine

tony123 · 2008-07-21 05:00:48

Let

and be prime numbers

such that

and

Determine all possible values of

.

Last edited by tony123 (2008-07-21 05:01:18)

ZHero · 2008-07-22 06:53:25

I've found one possible answer and i wonder if there are others too..

or
with being the greatest of all!

Now..

means that should be somewhere around !
using the first set of inequalities, we notice that can be somewhere round 17 which finally lets us conclude that may either be 7 or 5 giving possible values of as 3 or 2 !

Last edited by ZHero (2008-07-22 07:16:37)

ZHero · 2008-07-22 07:14:25

Now, if we select

then we get which doesn't hold for any prime & !
The same is true for too!
But, for , we get which is satisfied for !

Finally..

are the numbers we're looking for and we can find the value of the required expression!

Last edited by ZHero (2008-07-22 07:21:02)

ZHero · 2008-07-22 07:30:54

I understand that there's nothing so TECHNICAL about this method of mine..
Its just simple logic being put into the problem to guess/reduce the possible values of a, b, c & d and then verifying the final value!
I wonder if there's a more DIRECT method!?

From above, a possible value of

Last edited by ZHero (2008-07-22 07:32:45)

tony123 · 2008-07-23 05:08:00

thank you ZHero

nice work
and

Since a^2-b^2 +c^2-d^2 is odd, one of the primes a, b, c and d must be 2,
and in view of a > 3b > 6c > 12d we must have d = 2.

Math Is Fun Forum

#1 2008-07-21 05:00:48

Determine

#2 2008-07-22 06:53:25

Re: Determine

#3 2008-07-22 07:14:25

Re: Determine

#4 2008-07-22 07:30:54

Re: Determine

#5 2008-07-23 05:08:00

Re: Determine

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