Mixed sums of squares and triangular numbers (III)
| dc.creator | Oh, Byeong-Kweon | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2008-04-23 | |
| dc.date | 2009-02-07 | |
| dc.date.accessioned | 2026-07-07T12:38:24Z | |
| dc.date.available | 2026-07-07T12:38:24Z | |
| dc.description | In this paper we confirm a conjecture of Sun which states that each positive integer is a sum of a square, an odd square and a triangular number. Given any positive integer m, we show that p=2m+1 is a prime congruent to 3 modulo 4 if and only if T_m=m(m+1)/2 cannot be expressed as a sum of two odd squares and a triangular number, i.e., p^2=x^2+8(y^2+z^2) for no odd integers x,y,z. We also show that a positive integer cannot be written as a sum of an odd square and two triangular numbers if and only if it is of the form 2T_m (m>0) with 2m+1 having no prime divisor congruent to 3 modulo 4. | |
| dc.identifier | https://arxiv.org/abs/0804.3750 | |
| dc.identifier | http://arxiv.org/abs/0804.3750 | |
| dc.identifier | J. Number Theory 129(2009), no.4, 964-969 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218749 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11E25; 05A05; 11D85; 11P99; 11Y11 | |
| dc.title | Mixed sums of squares and triangular numbers (III) | |
| dc.type | text |