perplexus.info :: Numbers : Valid Prime Number Pairs

Valid Prime Number Pairs (Posted on 2023-08-03)

Find all possible pairs (m,n) of prime numbers that satisfy this equation:

            2^m = 2^n-2 + n!

Prove that there are no other valid pair that conform to the given conditions.

*** Computer program assisted solutions are welcome, but a semi-analytic (hand calculator and p&p solution) is preferred.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(m,n) = {(3,3), (7,5)} constitutes all possible solutions to the given problem.
For an explanation, refer to the solution submitted by Brian Smith in this location..

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

Subject	Author	Date
Solution	Brian Smith	2023-08-03 12:11:07
Computer Solution	Larry	2023-08-03 11:41:22

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