perplexus.info :: Just Math : Factorials and 2 powers

Factorials and 2 powers (Posted on 2021-08-13)

Find all pairs (k,n) of positive integers such that

k!=(2ⁿ-1)(2ⁿ-2)(2ⁿ-4)...(2ⁿ-2^n-1)

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Answer

Comment 5 of 5 |

The only possible positive integer pairs that satisfy the equation are given by:

(k,n)=(1,1), (3,2)

If nonnegative integer pairs were asked for, we would have an additional pair (I n) as (0,1)

Edited on May 11, 2022, 10:05 pm

Posted by K Sengupta on 2022-05-11 22:03:37

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info