🧵 Number theory
Anonymous at Fri, 10 May 2024 04:03:09 UTC No. 16168493
This problem was given to me by Wendy Krieger: 'can you show that two random fibonacci numbers where the index is coprime, are in fact coprime?'
Anonymous at Fri, 10 May 2024 04:55:06 UTC No. 16168536
Wouldn't they need to be random *distinct* Fibonacci numbers? 8 is the 7th Fibonacci number. 7 is coprime with 7, but 8 isn't coprime with 8.
Ostensibly 8 could be randomly selected twice among all Fibonacci numbers. Albeit the odds of that happening are 0.
Anonymous at Fri, 10 May 2024 05:00:17 UTC No. 16168543
>>16168536
I believe she means that for any two coprime natural numbers m and n, F_m and F_n are coprime. It's not the most rigorous phrasing.
Anonymous at Fri, 10 May 2024 05:03:20 UTC No. 16168548
>>16168536
Also, 7 is not coprime with 7; 7 is a factor of itself not equal to 1.
is this even possible? at Fri, 10 May 2024 06:28:46 UTC No. 16168621
idk if i am sure but is this even possible to do that?
Anonymous at Fri, 10 May 2024 06:32:30 UTC No. 16168624
>>16168621
Wendy told me she proved it back in the '80s.
🗑️ Anonymous at Fri, 10 May 2024 06:55:55 UTC No. 16168644
>>16168548
You're right. I was thinking of the definition of prime, not coprime.
0 then.
go to bed finnboltz at Fri, 10 May 2024 11:28:07 UTC No. 16168847
https://www.cut-the-knot.org/arithm
If (m,n)=1, then (F_m,F_n) = F_1 = 1. This is just a weak version of this theorem.
Anonymous at Fri, 10 May 2024 11:38:25 UTC No. 16168863
>>16168847
Do I know you on Discord?