(a, b, c); a*b = 1 (mod c)

 
 
Consider   (2, \; 3,  \;5)

(2\times 3) \;\equiv \; 1 \; \pmod{5}
(3\times 5) \;\equiv \; 1 \; \pmod{2}
(5\times 2) \;\equiv \; 1 \; \pmod{3}

Can you find another triplet with the same property?

that is,

(a, \; b, \; c)   such that

(a\cdot b) \;\equiv \; 1 \; \pmod{c}
(b\cdot c) \;\equiv \; 1 \; \pmod{a}
(c\cdot a) \;\equiv \; 1 \; \pmod{b}

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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