A New Property of Triangular Numbers

Rahil Miraj

doi:https://doi.org/10.14445/22315373/IJMTT-V58P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 58 | Number 3 | Year 2018 | Article Id. IJMTT-V58P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P526

A New Property of Triangular Numbers

Rahil Miraj

Citation :

Rahil Miraj, "A New Property of Triangular Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 3, pp. 192-194, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P526

Abstract

If a Triangular number ( except 1 and 3 ) is expressed as the sum of its consecutive partitions starting from unit, then among the partitions, one can find at least one pair of numbers, which give the same remainder when divided by the greatest integer not exceeding the square root of that Triangular number.

Keywords

Triangular number; Partitions; Floor function or greatest integer function; Pigeon Hole Principle.

References

[1] Wikipedia.
[2] David M. Burton, Elementary Number Theory, Macgraw Hill Education, (2016) .