# Simple Proof of Beal's Conjecture

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• Aug 11th 2010, 03:31 PM
chiph588@
Quote:

Originally Posted by MrAwojobi
MrAwojobi
Hi all, I have added an extra equation to this revised proof to show why the Pythagorean triples do not obey Beal's equation

SIMPLE PROOF OF BEAL’S CONJECTURE
Beal’s Conjecture
Beal’s conjecture states that if A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
Examples
...............................Common Prime Factor
2^3 + 2^3 = 2^4 => 2
2^9 + 8^3 = 4^5 => 2
3^3 + 6^3 = 3^5 => 3
3^9 + 54^3 = 3^11 => 3
27^4 + 162^3 = 9^7 => 3
7^6 + 7^7 = 98^3 => 7
33^5 + 66^5 = 33^6 => 11
34^5 + 51^4 = 85^4 => 17
19^4 + 38^3 = 57^3 => 19

Primitive Pythagorean Triples
A primitive Pythagorean triple is one in which the integer lengths of the right angled triangle do not have a common prime factor. Examples are….
( 3 , 4 , 5 ) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)
(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)
(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)
Hence the reason why x, y and z in Beal’s conjecture equation have to be greater than 2. These triples do not obey Beal's equation because of
the unique factorisation of a^2+b^2=c^2 to a^2 = (c+b)(c-b)

Simple Proof
It should be clear that each term in the equation A^x + B^y = C^z can be broken down into the product of its prime factors after numbers have been substituted into it. Thus the equation could be rewritten as abcde + fghij = klmno for instance, where a,b,c,d,e,f,g,h,i,j,k,l,m,n,o are prime . It isn’t difficult to see that
the 1st product + the 2nd product = the 3rd product
if and only if the left hand side of the equation can be factorised, i.e. rewritten in the form P(Q + R) where P,Q and R are positive integers. This will therefore guarantee that A, B and C share a common prime factor.

You have a fundamental flaw in your proof. You need to start over from scratch. Also what if x=y=z=1 or x=y=2, z=1, etc?

If you're so confident in your proof, why are you telling us it if it can win you \$100,000? Aren't you afraid of your "proof" being stolen?
• Aug 11th 2010, 04:35 PM
MrAwojobi
chiph588@

how can it be stolen when the evidence is right here with dates and time? Maybe if the thief is a time traveller then that would be possible. But then if he was a time traveller I'm sure he or she will be up to something more sinister than stealing my proof.
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