Linear diophantine equation

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Linear Diophantine equation has the form:

where x, y, z ... are integers unknown and a, b, c ... and K is an integer right side. The calculator can solve linear Diophantine equation with positive coefficients and the positive right side (i.e., in the natural number range).

E.g. by equation 28x + 30y + 31z = 365 we can examine how many months in a year can have 28, 30 and 31 days. Similarly, e.g. equation 2019 = 16x + 3y solves decomposition of natural number 2019 into base 16, 3 ...

Examples of Linear Diophantine equation: