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A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

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 ...

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 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 ...

A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. ...

A number which is simultaneously a pentagonal number P_n and triangular number T_m. Such numbers exist when 1/2n(3n-1)=1/2m(m+1). (1) Completing the square gives ...

A number which is simultaneously a heptagonal number H_n and triangular number T_m. Such numbers exist when 1/2n(5n-3)=1/2m(m+1). (1) Completing the square and rearranging ...

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 term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...