Problem 399

[mctrafik]

Wanted to say a couple things:

So the goal is to skip the "not squarefree" as opposed to "squareful" numbers from the fibonacci sequence, right? That's one clarification I had.
I wanted to know if someone found it useful to look into squareful numbers for this one.

And as always, not asking for any solutions here, but a keyword as a hint in the general direction would be appreciated. Got the problem down to a few thousand candidates but have no way of even checking if one is correct.

Thank you.

[hk]

Hints in any direction are not the purpose of this forum.
The purpose of this forum is to clear out probable misunderstandings of the problem and to clear out things that might be unclear from the wording of it.

[luckyrodman]

hello... mctrafik, nice to meet you

I reverse your ID, it's kifartcm

truncating the last two characters, it is kifart.

It reminds me of something, I think it's not a coincidence, right?

[thundre]

So the goal is to skip the "not squarefree" as opposed to "squareful" numbers from the fibonacci sequence, right? That's one clarification I had.
I wanted to know if someone found it useful to look into squareful numbers for this one.

"Squareful" and "not squarefree" mean exactly the same thing.

Since the question concerns the intersection of squarefree and Fibonacci numbers, it would be advisable to research both of those topics.

[mctrafik]

Squareful numbers are numbers for which at least one prime factor exponent is 2, thus are not squarefree numbers, not to be confused with squarefull numbers, numbers for which each prime factor exponent is at least 2.

- From oeis wiki.

[Marcus_Andrews]

A squarefree number has no repeated factors anywhere in its prime decomposition.

A squareful number is the same as a non-squarefree number -- which means it has at least one repeated factor somewhere in its prime decomposition.
http://mathworld.wolfram.com/Squareful.html

[luckyrodman]

hello...

In the problem thread, it is mentioned that this problem is based on a unproved conjecture.

But so far none of the development members give an explanation.

[hk]

No need to give one if you would have read the thread properly: because the "conjecture" has been verified for primes far beyond the limit needed for this problem. (see ignat_s's post)
The nice thing with Project Euler is that you can leave most of the comments to the members themselves, without admin interference. .

[sivakd]

@hk: what about mclo's comment "(Edit2) @ignat_s:" ?

[hk]

We'll look into it.

[epiclolz]

nitpicking: halfway through the third line there is a typo
"8 is DIVIBLE by 4"

[hk]

Thanks. Fixed.