+0  
 
0
98
6
avatar

Determine the number of fractions in the pattern below that are expressed in lowest terms.

 

1/2019, 2/2019, 3/2019, ..., 2019/2019

 Jul 19, 2022

Best Answer 

 #3
avatar+37 
+1

The problem basically asks how many numbers are relatively prime to 2019, as those that are cannot be further simplified.

 

Thus, Euler's Totient Function gives, (1 - 1/3)(1 - 1/673) 2019 = 1344.

 

@CPhill, for instance, 6/2019 gives 3/673 :)

 Jul 19, 2022
 #1
avatar+1155 
+4

The denominator is not needed. Cancel that out, to get 

 

1,2,3,...,2019

 

So, there are 2019 integers,

I believe.

 Jul 19, 2022
 #2
avatar+124676 
0

See below......!!!!

 

 

cool cool cool

 Jul 19, 2022
edited by CPhill  Jul 19, 2022
 #3
avatar+37 
+1
Best Answer

The problem basically asks how many numbers are relatively prime to 2019, as those that are cannot be further simplified.

 

Thus, Euler's Totient Function gives, (1 - 1/3)(1 - 1/673) 2019 = 1344.

 

@CPhill, for instance, 6/2019 gives 3/673 :)

SupersonicMan12 Jul 19, 2022
 #4
avatar+124676 
+2

Thx, Supersonic Man 12   !!!!!

 

That's a great answer !!!!

 

 

cool cool cool

CPhill  Jul 19, 2022
 #5
avatar+37 
0

Hi, CPhill!! I'm new to web2.0calc :) 

SupersonicMan12  Jul 19, 2022
 #6
avatar+124676 
+1

Welcome aboard   !!!!

 

 

cool cool cool

CPhill  Jul 19, 2022

23 Online Users

avatar