Equation : x^n + y^n + z^n = 0 (mod p)

 
 
x^{n} \; + \; y^{n} \; + \; z^{n} \; \equiv \; 0 \; ( \, \bmod{ \, p \, } \, )

 
Solutions

For   n = 3.     The only values of   p   are   7   and   13

For   n = 5,     p =   11,   41,   71,   101       [   verified up to   10^4   ]

For   n = 7,     p   =   29,   71,   113,   491

 

Can you find other solutions?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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