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A conjecture for the eigenvalues of modular forms under Hecke operators.

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

A solid dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces composed of all the irregular ...

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

A totalistic cellular automaton is a cellular automata in which the rules depend only on the total (or equivalently, the average) of the values of the cells in a ...

The best known packings of equilateral triangles into an equilateral triangle are illustrated above for the first few cases (Friedman). The best known packings of equilateral ...

Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...

A Wagstaff prime is a prime number of the form (2^p+1)/3 for p a prime number. The first few are given by p=3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, ...

A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper ...