• Corpus ID: 230433971

Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers

@inproceedings{Pletser2020RecurrentRF,
  title={Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers},
  author={Vladimir Pletser},
  year={2020}
}
We search for triangular numbers that are multiples of other triangular numbers. It is found that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers that are triangular numbers and recurrent relations are deduced theoretically. If the multiplier is a squared integer, there is either one or no solution, depending on the multiplier value. 

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References

SHOWING 1-10 OF 16 REFERENCES

A reconstruction of Joncourt's table of triangular numbers (1762)

This is an analysis and reconstruction of Joncourt's table of triangular numbers, one of only very few such tables, which was an alternative to other methods for the computation of squares, the

Triangular Numbers and Elliptic Curves

Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solutions (r, s, t) in the function field Q(m, n) of the pair of equations r(r + 1)/2 = ms(s + 1)/2 r(r

History of the Theory of Numbers

THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H.

History of the Theory of Numbers

THE arithmetical questions treated by Diophantus of Alexandria, who flourished about the year 250 A.D., included such problems as the solution of the equationsHistory of the Theory of Numbers.By

L’Équation uv = w2 en Nombres Triangulaires (French)

  • Publ. Inst. Math. Beograd,
  • 1963

The decomposition of triangular numbers

Quotients of triangular numbers

Triangular Number

  • From MathWorld-A Wolfram Web Resource

Some reanrks on Triangular Numbers

  • Numer Theory with an Emphasis on the Markoff Spectrum
  • 1993

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "the Educational Times"

  • Volume 75,
  • 1901