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The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

Donaldson (1983) showed there exists an exotic smooth differential structure on R^4. Donaldson's result has been extended to there being precisely a continuum of ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

The q-series identity product_(n=1)^(infty)((1-q^(2n))(1-q^(3n))(1-q^(8n))(1-q^(12n)))/((1-q^n)(1-q^(24n))) = ...

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...