Problem 243

[chrisb555]

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]

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

"Proportion" would have been a better word than "ratio".

[chrisb555]

Thanks Ed - that's very clear

[Oliver1978]

So primes always give 1?

[Georg]

Yes.

[frodenburg]

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]

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]

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]

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.