Not Every Number is the Sum or Difference of Two Prime Powers
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Theorem
Not every positive integer can be expressed in the form $p^m \pm q^n$ where $p, q$ are prime and $m, n$ are positive integers.
Proof
What is to be demonstrated is that there exist odd integers which cannot be expressed as $2^m \pm q^n$.
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Sources
- 1975: Frederick R. Cohen and J.L. Selfridge: Not Every Number is the Sum or Difference of Two Prime Powers (Math. Comp. Vol. 29, no. 129: pp. 79 – 81) www.jstor.org/stable/2005463