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A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

A number which is simultaneously pentagonal and hexagonal. Let P_n denote the nth pentagonal number and H_m the mth hexagonal number, then a number which is both pentagonal ...

A number which is simultaneously octagonal and heptagonal. Let O_m denote the mth octagonal number and H_n the nth heptagonal number, then a number which is both octagonal ...

A number which is simultaneously octagonal and pentagonal. Let O_n denote the nth octagonal number and P_m the mth pentagonal number, then a number which is both octagonal ...

A number which is simultaneously octagonal and triangular. Let O_n denote the nth octagonal number and T_m the mth triangular number, then a number which is both octagonal ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...