Mathematica treats equations as logical statements. If you type in an equation like x^2+3x==2, Mathematica interprets this as a logical statement which asserts that x^2+3x is ...

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

Cubics is an option for functions that involve solving algebraic equations, that specifies whether explicit forms for solutions to cubic equations should be given.

Quartics is an option for functions that involve solving algebraic equations that specifies whether explicit forms for solutions to quartic equations should be given.

TransformationFunctions is an option for Simplify and FullSimplify which gives the list of functions to apply to try to transform parts of an expression.

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

Modulus -> n is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

PolynomialMod[poly, m] gives the polynomial poly reduced modulo m. PolynomialMod[poly, {m_1, m_2, ...}] reduces modulo all of the m_i.

Mathematica has fundamental support for both explicit complex numbers and symbolic complex variables. All applicable mathematical functions support arbitrary-precision ...

When you give a list of equations to Solve, it assumes that you want all the equations to be satisfied simultaneously. It is also possible to give Solve more complicated ...