## Problem 243

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chrisb555
Posts: 2
Joined: Fri Jan 09, 2009 5:27 am

### Problem 243

Hi,

Could someone clarify for me what is meant by "ratio of its proper fractions that are resilient"?
What I understand to be the ratio of the resilient fractions for d=12 is :
(1/12):(5/12):(7/12):(11/12)
and I calculate this to be 144/385. So clearly my understanding is different to yours.
Could you clarify?

Thanks,
Chris

ed_r
Posts: 1009
Joined: Sun Jul 29, 2007 9:57 am

### Re: Problem 243

R(d) is the number of resilient proper fractions, divided by d-1.

"Proportion" would have been a better word than "ratio".
!647 = &8FDF4C

chrisb555
Posts: 2
Joined: Fri Jan 09, 2009 5:27 am

### Re: Problem 243

Thanks Ed - that's very clear

Oliver1978
Posts: 165
Joined: Sat Nov 22, 2014 9:13 pm
Location: Erfurt, Germany

### Re: Problem 243

So primes always give 1?
49.157.5694.1125

Georg
Posts: 157
Joined: Mon Jan 21, 2008 7:00 am
Location: Mannheim, Germany
Contact:

### Re: Problem 243

Yes.

frodenburg
Posts: 3
Joined: Sun Nov 25, 2018 10:25 am

### Re: Problem 243

How come R(12) is the lowest resilient denominator below 40% and that there is ANOTHER lowest denominator below 16%?
What is meant with minimal and what should I be looking for? Is my english the issue?

Animus
Posts: 1648
Joined: Sat Aug 16, 2014 12:23 pm

### Re: Problem 243

You can find a lower resilent fraction for higher denominators, the question is how big the denominator must get in order to get the resilent fraction below the given treshold for the very first time. That's no contradiction.

PS: Your nickname sounds german. If english is an issue and german is fine, you can PM me "auf Deutsch".

frodenburg
Posts: 3
Joined: Sun Nov 25, 2018 10:25 am

### Re: Problem 243

So in this case of lowest below 4/10 means that the 4 is fixed and the lowest x of D(x) with numerator 4 is to be found?
I'll try that and see.

frodenburg
Posts: 3
Joined: Sun Nov 25, 2018 10:25 am

### Re: Problem 243

By the way, I am Dutch, so German does not really help
Thanks for your explanation though, I give it a try to see if I understood.