Back to Search
Start Over
Finite sequences of integers expressible as sums of two squares.
- Source :
-
International Journal of Number Theory . Aug2024, Vol. 20 Issue 7, p1755-1766. 12p. - Publication Year :
- 2024
-
Abstract
- This paper is concerned with finite sequences of integers that may be written as sums of squares of two nonzero integers. We first find infinitely many integers n such that n , n + h and n + k are all sums of two squares where h and k are two arbitrary integers, and as an immediate corollary obtain, in parametric terms, three consecutive integers that are sums of two squares. Similarly we obtain n in parametric terms such that all the four integers n , n + 1 , n + 2 , n + 4 are sums of two squares. We also find infinitely many integers n such that all the five integers n , n + 1 , n + 2 , n + 4 , n + 5 are sums of two squares, and finally, we find infinitely many arithmetic progressions, with common difference 4, of five integers all of which are sums of two squares. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ARITHMETIC series
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 20
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 178505213
- Full Text :
- https://doi.org/10.1142/S1793042124500866