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Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.

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Feasibility of constrained multivariable diophantine equations

Let $d$ be day, $m$ be month and $y$ be year fields of a date. I want to find few dates of format $$(d^2\, mod\,\, 2 + (my + d^3) \,mod \,4) = 2$$ Is there a method to solve this type of equation or …
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1 vote

Feasibility of constrained multivariable diophantine equations

Note: I am answering my own question According to Hilbert's tenth problem, there exists no general algorithm to say whether there exist integer solutions for a given Diophantine equation or not.
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