a^n + b^n + c^n = x^n + y^n, n = 1,3

 
 
(1)   Find a few solutions to the system

a^3 + b^3 + c^3 = x^3 + y^3 1

  
where   a, b, c, x, y   are positive integers.

 
(2)   Prove that there are infinitely many solutions in positive integers, whose greatest common divisor is equal to 1
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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