Fibonacci numbers that are not sums of two prime powers

DOI10.1090/S0002-9939-05-07827-5zbMath1113.11011OpenAlexW2124475025MaRDI QIDQ4663437

Florian Luca, Pantelimon Stănică

Publication date: 31 March 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-07827-5

zbMATH Keywords

Fibonacci numbersarithmetic progressionssums of powers

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Arithmetic progressions (11B25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Sequences (mod (m)) (11B50)

Related Items (6)

EIGHT CONSECUTIVE POSITIVE ODD NUMBERS NONE OF WHICH CAN BE EXPRESSED AS A SUM OF TWO PRIME POWERS ⋮ On the integers of the form $p^{2}+b^{2}+2^{n}$ and $b_{1}^{2}+b_{2}^{2}+2^{n^{2}}$ ⋮ On the density of integers of the form \(2^k + p\) in arithmetic progressions ⋮ Covers of the integers with odd moduli and their applications to the forms $x^{m}-2^{n}$ and $x^{2}-F_{3n}/2$ ⋮ ON THE DENSITY OF INTEGERS OF THE FORM (p−1)2⁻ⁿ IN ARITHMETIC PROGRESSIONS ⋮ Unnamed Item

Cites Work

• Not Every Number is the Sum or Difference of Two Prime Powers
• On integers which are not differences of two powers
• On integers not of the form ±𝑝^{𝑎}±𝑞^{𝑏}
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