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Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976 (Gropp 1990), and several ...

There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. ...

An unordered factorization is a factorization of a number into a product of factors where order is ignored. The following table lists the unordered factorizations of the ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

Although Bessel functions of the second kind are sometimes called Weber functions, Abramowitz and Stegun (1972) define a separate Weber function as ...

The quasiperiodic function defined by d/(dz)lnsigma(z;g_2,g_3)=zeta(z;g_2,g_3), (1) where zeta(z;g_2,g_3) is the Weierstrass zeta function and lim_(z->0)(sigma(z))/z=1. (2) ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

An e-prime is a prime number appearing in the decimal expansion of e. The first few are 2, 271, 2718281, ...