+0

# Fractions

0
224
6

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

#3
+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
+1161
+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
+126653
0

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

Jul 19, 2022
edited by CPhill  Jul 19, 2022
#3
+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 :)

SupersonicMan12 Jul 19, 2022
#4
+126653
+2

Thx, Supersonic Man 12   !!!!!

CPhill  Jul 19, 2022
#5
+37
0

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

SupersonicMan12  Jul 19, 2022
#6
+126653
+1

Welcome aboard   !!!!

CPhill  Jul 19, 2022