FindInstance[expr, vars] finds an instance of vars that makes the statement expr be True. FindInstance[expr, vars, dom] finds an instance over the domain dom. Common choices ...

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

PowerModList[a, s/r, m] gives a list of all x modulo m for which x^r \[Congruent] a^s mod m.

Booleans represents the domain of Booleans, as in x \[Element] Booleans.

PowersRepresentations[n, k, p] gives the distinct representations of the integer n as a sum of k non-negative p\[Null]^th integer powers. FPowersRepresentations[n, {a_1, a_2, ...

SatisfiabilityInstances[bf] attempts to find a choice of variables that makes the Boolean function bf yield True. SatisfiabilityInstances[expr, {a_1, a_2, ...}] attempts to ...

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be ...

ChineseRemainder[{r_1, r_2, ...}, {m_1, m_2, ...}] gives the smallest non-negative x that satisfies all the integer congruences x mod m_i = r_i mod m_i.