SOLUTION: How many fractions of the form a/b are there, where a and b have no common factors larger than 1, such that b = a + 6 and a/b < 2017/2023?

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Question 1137879: How many fractions of the form a/b are there, where a and b have no common factors
larger than 1, such that b = a + 6 and a/b < 2017/2023?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Ans +highlight%28+2022+%29+
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Workout:
(Assumes a and b are any integers):


For +a%3E=0+:

a/(a+6) < 2017/2023
2023a < 2017(a+6)
2023a < 2017a + 12102
6a < 12102
a < 2017

So that gives the 2017 fractions 0/6, 1/7, ..., 2016/2022

Now for +a%3C0+ :
-1/5, -2/4, -3/3, -4/2 and -5/1 are all < 2017/2023
This is an additional 5 fractions.

Continuing with negative integers:
-6/0 is undefined
-7/-1 is 7 > 2017/2023

For all other negative integers a/(a+6) > 1 > 2017/2023 (the magnitude of (a) is greater than (a+6) for all these numbers)

2017 + 5 = 2022