Search Results for ""

A number which is simultaneously a nonagonal number N_m and heptagonal number Hep_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=1/2n(5n-4). (1) Completing the ...

A number which is simultaneously a nonagonal number N_m and octagonal number O_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=n(3n-2). (1) Completing the ...

A number which is simultaneously a nonagonal number N_m and pentagonal number P_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=1/2n(3n-1). (1) Completing the ...

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

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 ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...