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Abstract: In this paper we study mixed sums of primes and linear recurrences. We showthat if m=2mod 4 and m+1 is a prime then $m^{2^n-1}-1-m-1 ot=m^n+p^a$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 sumsu m+au n m,n=1,2,3,

. are distinct. One of our conjectures states that anyinteger n>4 can be written as the sum of an odd prime, an odd Fibonacci numberand a positive Fibonacci number.



Author: Zhi-Wei Sun

Source: https://arxiv.org/







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