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A number which is simultaneously a nonagonal number N_m and a triangular number T_n and therefore satisfies the Diophantine equation. 1/2m(7m-5)=1/2n(1+n). (1) Completing the ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

Given an integer e>=2, the Payam number E_+/-(e) is the smallest positive odd integer k such that for every positive integer n, the number k·2^n+/-1 is not divisible by any ...

The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30). The unit pentagonal ...

If G is a weighted tree with weights w_i>1 assigned to each vertex v_i, then G is perfectly weighted if the matrix M_G=[w_1 0 ... 0; 0 w_2 ... 0; | ... ... |; 0 0 ... ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

A Pythagorean quadruple is a set of positive integers a, b, c, and d that satisfy a^2+b^2+c^2=d^2. (1) For positive even a and b, there exist such integers c and d; for ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...