lhs := rhs assigns rhs to be the delayed value of lhs. rhs is maintained in an unevaluated form. When lhs appears, it is replaced by rhs, evaluated afresh each time.
Assuming[assum, expr] evaluates expr with assum appended to $Assumptions, so that assum is included in the default assumptions used by functions such as Refine, Simplify, and ...
CarmichaelLambda[n] gives the Carmichael function \[Lambda](n), defined as the smallest integer m such that k^m \[Congruent] 1 mod n for all k relatively prime to n.
DiscretePlot3D[expr, {i, i_min, i_max}, {j, j_min, j_max}] generates a plot of the values of expr when i runs from i_min to i_max and j runs from j_min to ...
Multinomial[n_1, n_2, ...] gives the multinomial coefficient (n_1 + n_2 + ...)!/(n_1! n_2! ...).
Rectangle[{x_min, y_min}, {x_max, y_max}] is a two-dimensional graphics primitive that represents a filled rectangle, oriented parallel to the axes. Rectangle[{x_min, y_min}] ...
StudentTDistribution[\[Nu]] represents a Student t distribution with \[Nu] degrees of freedom.StudentTDistribution[\[Mu], \[Sigma], \[Nu]] represents a Student t distribution ...
COperator[oper, arg_1, ...] is a symbolic representation of an operator.
CriticalSection[{var_1, var_2, ...}, expr] locks the variables var_i with respect to parallel computation, evaluates expr, then releases the var_i.
FiniteAbelianGroupCount[n] gives the number of finite Abelian groups of order n.