A Clairaut equation is a first-order equation of the form A remarkable feature of this nonlinear equation is that its general solution has a very simple form. This is an ...

A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

BitSet[n, k] sets to 1 the bit corresponding to the coefficient of 2^k in the integer n.

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

BitLength[n] gives the number of binary bits necessary to represent the integer n.

BitShiftLeft[n, k] shifts the binary bits in the integer n to the left by k places, padding with zeros on the right.BitShiftLeft[n] shifts one bit to the left.

DigitCount[n, b, d] gives the number of d digits in the base-b representation of n. DigitCount[n, b] gives a list of the numbers of 1, 2, ..., b - 1, 0 digits in the base-b ...

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

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

Mathematica provides many options for styling the cells that appear in notebooks. Some of the more common styling options are available directly from the Format menu. All ...