Here are just a few of them (you may wish to try proving them)
where the sequence of signs repeats with period 3
As I said, fascinating!
Thank goodness can show these values easily!
Can you prove that:
- if you have integers less than or equal to then there are always two of them which are relatively prime?
This problem comes from the biography of Paul Erdös, The Man Who Loved Only Numbers. Erdös posed this problem to Louis Pósa, who was 12 at the time and a child prodigy, and who solved it in about 10 minutes.
This is one of those problems where you can spend hours getting nowhere, and yet the proof is actually very simple 😕
Mathforge is one of the best sites for finding the latest news about mathematics. It reports from what seems like everywhere to tell you what is going on in the world of mathematics. If you are interested in maths then you really should be reading it.
Would you believe it? I have just seen that Richard Rusczyk’s the Search for Intelligence Continues. . . blog yesterday recommended Mathforge. I have been meaning to write this post for a week (honest :)) but he got there first.