perplexus.info :: Numbers : Smallest Prime Settlement

Smallest Prime Settlement (Posted on 2022-08-14)

Determine the minimum value of a prime number p such that there are positive integers x and y satisfying this equation:

         x² + p³ = y⁴

*** As an extra challenge only, solve this puzzle without using a computer program/spreadsheet aided method.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

6083^2 + 23^3 = 78^4
23 is the smallest prime that fits the bill.
For an explanation, refer to the solution submitted by broll in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Possible Solution	K Sengupta	2022-09-23 18:40:56
Possible Solution	broll	2022-08-14 12:07:50
computer solution	Charlie	2022-08-14 10:50:14

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info