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

EasyChair Preprint 12323

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

@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}}