Determine the number of fractions in the pattern below that are expressed in lowest terms.
1/2019, 2/2019, 3/2019, ..., 2019/2019
+37 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 :)
+1164 The denominator is not needed. Cancel that out, to get
1,2,3,...,2019
So, there are 2019 integers,
I believe.
+37 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 :)
