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ParthKohli
 2 years ago
Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]
ParthKohli
 2 years ago
Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Can you help me with that?

perl
 2 years ago
Best ResponseYou've already chosen the best response.0find all integer solutions

perl
 2 years ago
Best ResponseYou've already chosen the best response.0looks like we can factor something here

perl
 2 years ago
Best ResponseYou've already chosen the best response.0did you try to expand (a+b+c)^3

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3\]

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0So 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?

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

perl
 2 years ago
Best 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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0How would you solve it now?

perl
 2 years ago
Best ResponseYou've already chosen the best response.0where did you get this question, is it solvable?

perl
 2 years ago
Best ResponseYou've already chosen the best response.0well the simple approach is , equate terms

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, a solution is \((1,5,3)\)

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

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

perl
 2 years ago
Best ResponseYou've already chosen the best response.0ok, then you can go through all the cases , 09

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0I want a purely mathematical solution :
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