# Integer Diophantine equations solver

The equations have the following integer solutions:

**x*y*z =72**

x<y

y<z

s =x+y+z

x>0

y>0

z>0

x<y

y<z

s =x+y+z

x>0

y>0

z>0

**Number of solutions found: 7**

##### s_{1}=13, x_{1}=3, y_{1}=4, z_{1}=6

s_{2}=15, x_{2}=2, y_{2}=4, z_{2}=9

s_{3}=17, x_{3}=2, y_{3}=3, z_{3}=12

s_{4}=18, x_{4}=1, y_{4}=8, z_{4}=9

s_{5}=19, x_{5}=1, y_{5}=6, z_{5}=12

s_{6}=23, x_{6}=1, y_{6}=4, z_{6}=18

s_{7}=28, x_{7}=1, y_{7}=3, z_{7}=24

Write each equation on a new line or separate by a semicolon. Unknowns are a,b,c ... z. A

**Diophantine equation**is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are studied. An integer solution is a solution such that all the unknowns take integer values).

**Diophantine problems**have fewer equations than unknown variables and involve finding integers that work correctly for all equations.

## Examples of Diofant equations and problems:

ab=12

5x+7y=144

8x=27y+38

54=ab 90=bc

(((x-1)*2/3-1)*2/3-1)*2/3=y