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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

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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

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