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The batman curve is a piecewise curve in the shape of the logo of the Batman superhero originally posted on reddit.com on Jul. 28, 2011. It can written as two functions, one ...

A class of curve defined at integer values which hops from one value to another. Their name derives from the Greek word betaalphataurhoalphachiiotaomicronnu batrachion, which ...

If C_1, C_2, ...C_r are sets of positive integers and union _(i=1)^rC_i=Z^+, then some C_i contains arbitrarily long arithmetic progressions. The conjecture was proved by van ...

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as ...

Let T(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Define f_m(x)=product_(t in T(m))(x-t). (1) Then a ...

Let m>=3 be an integer and let f(x)=sum_(k=0)^na_kx^(n-k) be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not ...

The Baum-Sweet sequence is the sequence of numbers {b_n} such that b_n=1 if the binary representation of n contains no block of consecutive 0s of odd length, and b_n=0 ...

In April 1999, Ed Pegg conjectured on sci.math that there were only finitely many zerofree cubes, to which D. Hickerson responded with a counterexample. A few days later, Lew ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

The bead-sorting algorithm orders a list of a positive integers increasingly by representing numbers as a list of a 1s, where each 1 stands for a bead. The k initial integers ...