Question

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

Answer 1

hmmm

Answer 2

Can you help me with that?

Answer 3

find all integer solutions

Answer 4

looks like we can factor something here

Answer 5

did you try to expand
(a+b+c)^3

Answer 6

Whoo.

Answer 7

\[a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3\]

Answer 8

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?

Answer 9

\[(a + b + c)^3 = 3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2 + 100a + 10b + c \]

Answer 10

oh look at that

Answer 11

one second

Answer 12

(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

Answer 13

How would you solve it now?

Answer 14

not sure

Answer 15

where did you get this question, is it solvable?

Answer 16

well the simple approach is , equate terms

Answer 17

Yes, a solution is \((1,5,3)\)