perplexus.info :: Just Math : Given the Sum, Find the Sum

Given the Sum, Find the Sum (Posted on 2024-05-29)

Given that:

a+b+c= 2022

1/(a²⁰²²) + 1/(b²⁰²²) + 1/(c²⁰²²) = 1/2022
Find the value of:

1/(a²⁰²³) + 1/(b²⁰²³) + 1/(c²⁰²³)

**** Adapted from a problem appearing in Vietnamese IMO, 2022

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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

Question

Comment 2 of 2 |

The very first line of the official solution has

1/a+1/b+1/c=1/2022=1/(a+b+c)

Where does the first half of the equality come from?

Posted by Brian Smith on 2024-07-25 21:05:35

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info