Hello, what is the need to write an algorithm to solve an equation of the form ax + by + cz = n, where a, b, c and n are known?

Closed due to the fact that the question is too general for the participants Dmitriy Simushev , sercxjo , Vladimir Martyanov , VenZell , user194374 15 Feb '16 at 13:58 .

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  • one
    No. To uniquely solve a problem with three unknowns, three equations are needed. Learn mat. part. - Dmitriy Simushev
  • Brute force algorithm x, y, z. Only solutions will be many. - Vladimir Martyanov
  • @ Vladimir Martianov, formally, in the current formulation, the number of solutions is an infinite set. - Dmitriy Simushev February
  • @ Vladimir Martiyanov could you send it? - droft1312
  • one
    @ droft1312 write it for you and just send it to you? No, thanks. - Vladimir Martyanov

1 answer 1

Since in your equation ( ax + by + cz = n ) there are 3 unknowns, you need at least 2 more equations to solve, i.e. In fact, you should have a system of 3 equations to derive each of the unknowns.

After drawing up the system of equations, you can implement its solution, for example, by the method of Gauss or Kramer .

Or does your question touch on some other aspects (for example, deducing the dependence of one unknown on another / others)?

  • Hell, in my mind, it was possible to solve this equation by some sort. - droft1312
  • Well, for example, in the case of natural numbers, there may be no solutions at all. 2x + 3y + 4z = 1 . - andy.37
  • @ droft1312 Most likely, in the general case there should be an infinite number of solutions. - StateItPrimitive
  • @StateItPrimitive, not most likely, but absolutely certain. many solutions are not limited. - Dmitriy Simushev
  • one
    @ andy.37, 1x + 0y + 0z = 1 suitable solutions (1, 1, 1), (1, 1, 2), (1, 1, 3) .... the set of solutions is not limited. - Dmitriy Simushev February