## Problem 643

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vapor
Posts: 2
Joined: Sun Dec 31, 2017 3:02 pm

### Problem 643

What does g(100)=1031 mean in this problem?
Update: It seems that setting p<q gives the correct result.
Last edited by vapor on Sat Nov 17, 2018 7:27 pm, edited 1 time in total.

mscha
Posts: 6
Joined: Sat Jan 21, 2017 9:55 pm

### Re: Problem 643

I get f(10²) = 1037, not 1031, given the definition in the problem.
If I change the definition to require 1 ≤ p < q ≤ n instead of 1 ≤ p ≤ q ≤ n, then I get 1031. (That excludes (2,2), (4,4), (8,8) ... (64,64).)
So which is wrong, the definition or the example?

MHealy
Posts: 40
Joined: Sat Nov 17, 2012 11:32 pm

### Re: Problem 643

mscha wrote:
Sat Nov 17, 2018 7:25 pm

So which is wrong, the definition or the example?
The definition is wrong; the example values are correct. (Based on the expected answer.)
Last edited by MHealy on Sat Nov 17, 2018 7:48 pm, edited 1 time in total.

hk
Posts: 10806
Joined: Sun Mar 26, 2006 10:34 am
Location: Haren, Netherlands

### Re: Problem 643

It should read $1\le p\lt q\le n$. Problem edited.

vamsikal3
Posts: 113
Joined: Sat Oct 01, 2016 9:25 am

### Re: Problem 643

There is a minor typo in the problem:

For example, 24 and 40 and 2-friendly because ....

The correct text is: For example, 24 and 40 are 2-friendly because ....
my friend key --> 990813_OZPwQtCjkD6KlvxirOoTSZxccMFsuw1L

RobertStanforth
Posts: 1289
Joined: Mon Dec 30, 2013 11:25 pm

### Re: Problem 643

vamsikal3 wrote:
Sun Nov 18, 2018 9:35 am
The correct text is: For example, 24 and 40 are 2-friendly because ....
Thanks, Vamsi. This is fixed now.

Cot-O-Bus
Posts: 6
Joined: Thu Sep 27, 2018 10:18 am

### Re: Problem 643

Looks like expansion of PI-2, but...

HashFunction
Posts: 1
Joined: Mon Dec 31, 2018 3:01 pm

### Re: Problem 643

How come $$gcd(a,b)=2^t,t>0$$ , but with brute force I get f(100) = 1031 when t = 0 , that is $$gcd(a,b) = 2^0 = 1$$ , should t be >= 0 or am I wrong ?

hk