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

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

Guest Jul 19, 2022

#3**+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

#1**+4 **

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

1,2,3,...,2019

So, there are 2019 integers,

I believe.

nerdiest Jul 19, 2022

#3**+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