Mixed Sums of Primes and Other Terms
نویسندگان
چکیده
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 (m2n−1−1)/(m−1) 6= m+p for any n = 3, 4, . . . and prime power p. We also prove that if a > 1 is an integer, u0 = 0, u1 = 1 and ui+1 = aui + ui−1 for i = 1, 2, 3, . . ., then all the sums um + aun (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 and two positive Fibonacci numbers.
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Higher Correlations of Divisor Sums Related to Primes I: Triple Correlations
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