Editing Equation solving (section)

===Diophantine equations===
In [[Diophantine equations]] the solutions are required to be [[integer]]s. In some cases a brute force approach can be used, as mentioned above. In some other cases, in particular if the equation is in one unknown, it is possible to solve the equation for [[Rational number|rational]]-valued unknowns (see [[Rational root theorem]]), and then find solutions to the Diophantine equation by restricting the solution set to integer-valued solutions. For example, the polynomial equation
:<math>2x^5-5x^4-x^3-7x^2+2x+3=0\,</math>
has as rational solutions {{math|''x'' {{=}} −{{sfrac|1|2}}}} and {{math|''x'' {{=}} 3}}, and so, viewed as a Diophantine equation, it has the unique solution {{math|''x'' {{=}} 3}}.

In general, however, Diophantine equations are among the most difficult equations to solve.