Nonagonal Octagonal Number

A number which is simultaneously a nonagonal number N_m and octagonal number O_n and therefore satisfies the Diophantine equation


Completing the square and rearranging gives


Defining x=14n-5 and y=3m-1 gives the Pell-like equation


The first integral solutions in m and n are (m,n)=(1,1), (425, 459), (286209, 309141), (192904201, 208360351), ... (OEIS A048922 and A048923), giving the nonagonal octagonal numbers 1, 631125, 286703855361, 130242107189808901, ... (OEIS A048924).

See also

Nonagonal Number, Octagonal Number

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Sloane, N. J. A. Sequences A048922, A048923, and A048924 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Nonagonal Octagonal Number

Cite this as:

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

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