RMO 4

Number Theory Level 4

Find the number of positive integers < 3600 which are coprime to 3600.

2 solutions

Kalpok Guha
Dec 23, 2014

$\phi(3600)$ = $\phi(5^2)$ $\phi(3^2)$ $\phi(2^4)$

$\phi(5^2)=5^2-5^1$

$\phi(3^2)=3^2-3^1$

$\phi(2^4)=2^4-2^3$

Thus $\phi(3600)=20*6*8=960$

The answer is $960$

Are you Serious, Is this really a RMO problem?

Swapnil Das - 5 years, 10 months ago

I was also thinking this :P

Md Zuhair - 3 years, 8 months ago

I don't think it is a RMO problem.

Kalpok Guha - 3 years, 8 months ago

Without using Euler's Totient func. it will be RMO lvl question then

Md Zuhair - 3 years, 8 months ago

Rajarshi Chatterjee
Aug 24, 2014

use euler's phi function.

what i have done wrong if i count the factors of 3600 then subtract it from 3600

Dheeraj Agarwal - 6 years, 8 months ago

54 is not a factor of 3600 but gcd(54, 3600) != 1.

Vishal Antony - 6 years, 5 months ago

can u give a little more explanation

Ashwani Singh Tanwar - 6 years, 6 months ago

Yes exactly....

Jayakumar Krishnan - 6 years, 9 months ago

Hi.Rajarshi! Why didn't you show up in tution? (Dont think this a comment)

Chandrachur Banerjee - 6 years, 9 months ago

which tution

Kaustubh Miglani - 5 years, 11 months ago

the one i which u forgot your name ,ha ha

Chandrachur Banerjee - 5 years, 11 months ago