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The problem of finding in how many ways E_n a plane convex polygon of n sides can be divided into triangles by diagonals. Euler first proposed it to Christian Goldbach in ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

The probability that two events will both happen is hk, where h is the probability that the first event will happen, and k is the probability that the second event will ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.

A balanced incomplete block design (v, k, lambda, r, b) exists only for b>=v (or, equivalently, r>=k).

Consider a square wave f(x) of length 2L. Over the range [0,2L], this can be written as f(x)=2[H(x/L)-H(x/L-1)]-1, (1) where H(x) is the Heaviside step function. Since ...