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Prime Solutions to the Diophantine Equation 2^n = p^2 + 7

EasyChair Preprint 12323

4 pagesDate: February 29, 2024

Abstract

The Diophantine equation  2^n = p^2 + 7 for which p is prime and n
is integers with p > 0, is examined in this work. It is demonstrated
by examining the characteristics of the equation that the only solutions
meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7.
In order to analyze the above equation, it is necessary to look at the
properties of primes and how they relate to powers of two. These results
advance our knowledge of prime numbers and how they behave in certain
mathematical problems.

Keyphrases: Diophantine equation, Prime, integers

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:12323,
  author    = {Budee U Zaman},
  title     = {Prime Solutions to the Diophantine Equation 2^n = p^2 + 7},
  howpublished = {EasyChair Preprint 12323},
  year      = {EasyChair, 2024}}
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