Equation : a^4 – b^5 = c^5 – d^4

 
 

Let   a, \; b, \; c, \; d   be positive integers,   with   a \; \neq \; d,   and   b \; \neq \; c

Prove that if   a^4-b^5=c^5-d^4,   then twice the sum of the 5-th powers is a sum of two squares.

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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