Verify the properties of the Farey series given in Exercises 1, 2, and 3 for successive terms of your choice in the Farey series of order 100.
Exercise 1
Show that if k is a positive integer, then (15k + 4)/(10k + 3) is in lowest terms.
Exercise 2
Show that if a and b are relatively prime integers, then (a + 2b, 2a + b) = 1 or 3.
Exercise 3
Show that every positive integer greater than 6 is the sum of two relatively prime integers greater than 1.
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