Congruence properties of indices of triangular numbers multiple of other triangular numbers

@article{Pletser2021CongruencePO,
  title={Congruence properties of indices of triangular numbers multiple of other triangular numbers},
  author={Vladimir Pletser},
  journal={Open Journal of Mathematical Sciences},
  year={2021}
}
  • V. Pletser
  • Published 25 February 2021
  • Mathematics
  • Open Journal of Mathematical Sciences
For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple of other triangular numbers. We analyze the congruence properties of indices \(\xi\) of triangular numbers multiple of triangular numbers. Remainders in congruence relations \(\xi\) modulo \(k\) come always in pairs whose sum always equal \((k-1)\), always include 0 and \((k-1)\), and only 0 and \((k-1)\) if \(k\) is prime, or an odd power of a prime, or an even square plus one or an odd square… 
1 Citations

Tables from this paper

Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs

<jats:p>In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined

References

SHOWING 1-10 OF 20 REFERENCES

Searching for multiple of triangular numbers being triangular numbers. Research Gate, DOI: 10.13140/RG.2.2.35428.91527

  • 2021

Searching for Multiple of Triangular Numbers being Triangular Numbers, Preprint, to be submitted, February 2021

  • European Space Agency (ret.) Email address: PletserVladimir@gmail.com
  • 2021

Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers

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

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

Quotients of triangular numbers

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

The On-Line Encyclopedia of Integer Sequences

  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
TLDR
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.

Quotients of triangular numbers. The Mathematical Gazette

  • 2015