Not Every Number is the Sum or Difference of Two Prime Powers

DOI10.2307/2005463zbMath0296.10029OpenAlexW4249487603MaRDI QIDQ4049169

Frederick R. Cohen, John L. Selfridge

Publication date: 1975

Full work available at URL: https://doi.org/10.2307/2005463

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Congruences; primitive roots; residue systems (11A07) Software, source code, etc. for problems pertaining to number theory (11-04)

Related Items (20)

On a problem of Romanoff type ⋮ EIGHT CONSECUTIVE POSITIVE ODD NUMBERS NONE OF WHICH CAN BE EXPRESSED AS A SUM OF TWO PRIME POWERS ⋮ On integers of the forms \(k\pm 2^{n}\) and \(k2^{n}\pm 1\) ⋮ Partition into terms with prime numbers ⋮ An exploration of Nathanson's \(g\)-adic representations of integers ⋮ Chen's conjecture and its generalization ⋮ On the number of distinct prime factors of \(nj+a^hk\) ⋮ On Romanoff's constant ⋮ On integers which are the sum of a power of 2 and a polynomial value ⋮ On the integers of the form $p^{2}+b^{2}+2^{n}$ and $b_{1}^{2}+b_{2}^{2}+2^{n^{2}}$ ⋮ On the integers of the form \(p+b\) ⋮ Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers ⋮ Five consecutive positive odd numbers none of which can be expressed as a sum of two prime powers. II ⋮ Fibonacci numbers that are not sums of two prime powers ⋮ 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 integers not of the form Fn ± pa ⋮ Integral points on elliptic curves associated with generalized twin primes ⋮ On integers of the forms \(k-2^n\) and \(k2^n+1\) ⋮ On integers of the forms \(k^r-2^n\) and \(k^r2^n+1\).

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