java physics

There are two possible futures for our Universe, continual expansion (open and flat), or turn-around and collapse (closed). Note that flat is the specific case of expansion to ever slowly speeds aproaching zero velocity.

One of the key factors that determines which history is correct is the amount of mass/gravity for the Universe as a whole. If there is sufficient mass, then the expansion of the Universe will be slowed to the point of stopping, then retraction to collapse. If there is not a sufficient amount of mass, then the Universe will expand forever without stopping. The flat Universe is one where there is exactly the balance of mass to slow the expansion to zero, but not for collapse.

Before considering the integer equation x^3 + y^3 = z^3, it's 
worthwhile to briefly review the simple Pythagorean equation 
x^2 + y^2 = z^2.  For primitive solutions we can assume x,y,z
are pairwise coprime, x is odd and y is even.  The usual approach
is to re-write the equation as 
 
	    	
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Problem:
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Prove (or disprove?) that the only solutions of

                   ab = c (mod a+b)
                   ac = b (mod a+c)
                   bc = a (mod b+c)
 
	    	
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