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Finding the number of solutions to a diophantine equation
I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried:
Solve[{2*x + 3*y + z == 100, x > 0, y > 0, z > 0}, {x, y, z}, Integers]
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2 Answers
There are also power series methods for counting these.
SeriesCoefficient[
x^(1 + 2 + 3)/(1 - x^1)*1/(1 - x^2)*1/(1 - x^3), {x, 0, 100}]
(* Out[118]= 784 *)
See also "Supplement to 'Perplexities Related to Fourier's 17 Line Problem'."
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This should work:
sols = Solve[{2*x + 3*y + z == 100, x > 0, y > 0, z > 0},
{x, y, z}, Integers];
Length@sols
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Finding the number of solutions to a diophantine equation
I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried:
Solve[{2*x + 3*y + z == 100, x > 0, y > 0, z > 0}, {x, y, z}, Integers]
4,53333 gold badges3232 silver badges4848 bronze badges
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There are also power series methods for counting these.
SeriesCoefficient[
x^(1 + 2 + 3)/(1 - x^1)*1/(1 - x^2)*1/(1 - x^3), {x, 0, 100}]
(* Out[118]= 784 *)
See also "Supplement to 'Perplexities Related to Fourier's 17 Line Problem'."
60.9k22 gold badges107107 silver badges206206 bronze badges
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