Solving A Nice Diophantine Equation | Integer Solutions

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PLAYLISTS 🎵 :

[misterdubity]

I used Simon to get (3a+2)(3b+1) = 128; first factor is 2 mod 3, 2nd factor is 1 mod 3; When checking negative factors, their mod 3 values flip; eg factors (128*1) makes (a, b)=(42, 0) a+b=42; then flip to (-1 * -128) makes (a, b)=(-1, -43) a+b= -44. Solution set {-44, -23, -13, -9, 7, 11, 21, 42}

[ianfowler]

I know everybody has their favourite way of dealing with a rational expression where deg(numerator) = deg(denominator). Like adding 0 to the numerator and splitting. Also used, for example, in integration. Long division is often given a bum rap - claiming longer/more difficult. Not saying that you should change your method, but it is another option that is actually quite easy and short.

[mikelucas]

To make it simple, I set b=1 and took it from there; thus making a=10, coming up with a final answer of 11 and verifying it.

[shentakuki]

Patiently waiting for SyberMath to learn about the existance of Nier Automata 😁

[kentkoh]

Feel like a mouse being put into a maze. The question is: how the experience of finding a way out in this maze could help a mouse finding the way out in next one?

[yevgeno]

Your solution is wrong or at least is incomplete.

First of all, if you call this equation a Diophantine, then a, b must be > 0. So a = 0 or a = -1 are not solutions.
Secondly, you missed solution a=10, b=1 -> a+ b = 11.

Basically, there are 2 solutions: 2, 5 (sum = 7) and 10, 1 (sum = 11), if we're talking about Diophantine equation. If we're talking about an ordinal equation with integer solutions, then 0, 21 (21) and -1, -43 (-44) are solutions too.