Mixed sums of primes and other terms
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2009-01-20 | |
| dc.date | 2009-01-29 | |
| dc.date.accessioned | 2026-07-07T12:35:06Z | |
| dc.date.available | 2026-07-07T12:35:06Z | |
| dc.description | In this paper we study mixed sums of primes and linear recurrences. We show that if m=2(mod 4) and m+1 is a prime then $(m^{2^n-1}-1)/(m-1)\not=m^n+p^a$ for any n=3,4,... and prime power p^a. We also prove that if a>1 is an integer, u_0=0, u_1=1 and u_{i+1}=au_i+u_{i-1} for i=1,2,3,..., then all the sums u_m+au_n (m,n=1,2,3,...) are distinct. One of our conjectures states that any integer n>4 can be written as the sum of an odd prime, an odd Fibonacci number and a positive Fibonacci number. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0901.3075 | |
| dc.identifier | http://arxiv.org/abs/0901.3075 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217666 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11P32; 11A41; 11B37; 11B39; 11B75; 11Y99 | |
| dc.title | Mixed sums of primes and other terms | |
| dc.type | text |