Prime Solutions to the Diophantine Equation 2n = p2 +7

Budee U Zaman

doi:10.20944/preprints202402.1638.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 February 2024 / Approved: 28 February 2024 / Online: 28 February 2024 (13:55:57 CET)

The Diophantine equation for which p is prime 2^n = p^2 + 7 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.

integers; Diophantine Equation; prime number

Computer Science and Mathematics, Algebra and Number Theory

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Prime Solutions to the Diophantine Equation 2ⁿ = p² +7

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