perplexus.info :: Numbers : Three Linear Expressions Divide Three Exponent Expressions

Three Linear Expressions Divide Three Exponent Expressions (Posted on 2023-06-15)

Determine all possible integers n less than 10¹⁰⁰ that simultaneously satisfy these conditions:

n divides 2ⁿ
n - 1 divides 2ⁿ - 1
n - 2 divides 2ⁿ - 2

Note: As an extra challenge, determine a semi-analytic (simple calculator + p&p) solution to this problem.

**** Adapted from a problem appearing at a William Lowell Putnam Mathematics Competition

Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Solution: (Hide)

n= 4, 16, 65536 are the only possible solutions to the given problem for n < 10^100
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
re: There is another solution.	Charlie	2023-06-20 10:36:01
There is another solution.	Math Man	2023-06-19 12:58:25
Solution	Brian Smith	2023-06-15 10:24:05
computer exploration	Charlie	2023-06-15 09:41:33

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
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