Nonagonal Heptagonal Number

A number which is simultaneously a nonagonal number N_m and heptagonal number Hep_n and therefore satisfies the Diophantine equation


Completing the square and rearranging gives


Defining x=14n-5 and y=10m-3 gives the Pell-like equation


The first integral solutions in m and n are (m,n)=(1,1), (88, 104), (12445, 14725), (1767052, 2090804), ... (OEIS A048919 and A048920), giving the nonagonal heptagonal numbers 1, 26884, 542041975, 10928650279834, ... (OEIS A048921).

See also

Heptagonal Number, Nonagonal Number

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Sloane, N. J. A. Sequences A048919, A048920, and A048921 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Nonagonal Heptagonal Number

Cite this as:

Weisstein, Eric W. "Nonagonal Heptagonal Number." From MathWorld--A Wolfram Web Resource.

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