perplexus.info :: Numbers : Powering up the digits V

Powering up the digits V (Posted on 2022-08-26)

Each of α, β, γ, and δ corresponds to a nonzero digit, whether same or different, in positive integer base n.

Determine all possible values of n ≤ 100 such that this equation has at least one valid solution:

                  αβγδ = α^α + β^β + γ^γ + δ^δ

*** αβγδ corresponds to concatenation of the four digits.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The only solutions are: 3435(base 10), and: 6534(base 20)
For an explanation, refer to the solution submitted by Larry in this location.

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

Subject	Author	Date
computer-aided solution	Charlie	2022-08-26 09:09:28
Solution	Larry	2022-08-26 08:32:17

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 (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info