perplexus.info :: Numbers : All possible integer values of N

Home > Numbers

All possible integer values of N (Posted on 2023-10-02)

Determine all possible integer values of N that satisfy this equation:
(√5 + 2)^N + (√5 - 2)^N= 18

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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

Solution by inspection

| Comment 2 of 3 |

Since 5+4=9, then from inspection N=2 is a solution.

Since 5-4=1, the bases of the exponents are reciprocals, so N=-2 is also a solution. Also the LHS represents an even function.

For positive N, this is clearly also an increasing function, so there are no other solutions.

Posted by Jer on 2023-10-02 09:30:16

Please log in:

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