perplexus.info :: Numbers : Pythagorean Crossed Six Consecutive Digit Determination

Pythagorean Crossed Six Consecutive Digit Determination (Posted on 2023-05-24)

α, β, γ, δ, ε, ζ represents 6 consecutive digits (in any order) of base-N, where N is a positive integer.
It is known that:

(αβ)² + (γδ)² = (εζ)²

Determine the minimum value of N.
Note: αβ represents the concatenation of the digits and not their multiplication.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required minimum value of N is 10.
Only three solutions are possible from base 6 to base 1000. These are::
Base 10: 27^2 + 36^2 = 45^2
Base 14: 58^2 + 76^2 = 94^2 --> decimal 78^2 + 104^2 = 130^2
Base 16: 5A^2 + 78^2 = 96^2 --> decimal 90^2 + 120^2 = 150^2
The minimum base, N, is therefore: 10.
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
Solution	Larry	2023-05-24 13:56:23
computer solution	Charlie	2023-05-24 12:44:36

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 (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info