| An equation with any number of variables involving the basic arithmetic operations (addition, multiplication, and exponentiation) considering only integer solutions.
It has been proven that the problem of solving general Diophantine equations is undecidable. Some have no solutions, others have a finite number of solutions, some have an infinite number of solutions. Particular cases can be solved by one means or another, and Diophantine analysis is a major branch of mathematics and number theory. However, for many Diophantine equations, it is impossible to determine whether or not solutions even exist.
Example:
y2 = x3 + 1090
Solutions (probably incomplete):
x y
----------------------------
-9 19
-9 -19
-1 33
-1 -33
28,187,351 149,651,610,621
28,187,351 -149,651,610,621
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