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Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]
 one year ago
 one year ago
Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.0
Can you help me with that?
 one year ago

perlBest ResponseYou've already chosen the best response.0
find all integer solutions
 one year ago

perlBest ResponseYou've already chosen the best response.0
looks like we can factor something here
 one year ago

perlBest ResponseYou've already chosen the best response.0
did you try to expand (a+b+c)^3
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
\[a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3\]
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
So do we have to add \(3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2\) to both sides?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
\[(a + b + c)^3 = 3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2 + 100a + 10b + c \]
 one year ago

perlBest ResponseYou've already chosen the best response.0
(a+b+c)^3 = a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
How would you solve it now?
 one year ago

perlBest ResponseYou've already chosen the best response.0
where did you get this question, is it solvable?
 one year ago

perlBest ResponseYou've already chosen the best response.0
well the simple approach is , equate terms
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Yes, a solution is \((1,5,3)\)
 one year ago

perlBest ResponseYou've already chosen the best response.0
so if a^2 = 100 , b^2 = 10 , and c^2 = 1 , you have a solution
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I didn't mention that \((a,b,c)\) all must be singledigit numbers.
 one year ago

perlBest ResponseYou've already chosen the best response.0
ok, then you can go through all the cases , 09
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I want a purely mathematical solution :
 one year ago
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