Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently supposed that if the pair (a, b) is coprime and the pair (b, c) is coprime, then the pair (a, c) is coprime. You want to find a counterexample for your friend's statement. Therefore, your task is to find three distinct numbers (a, b, c), for which the statement is false, and the numbers meet the condition l ≤ a < b < c ≤ r. More specifically, you need to find three numbers (a, b, c), such that l ≤ a < b < c ≤ r, pairs (a, b) and (b, c) are coprime, and pair (a, c) is not coprime.

Question

Mathematics

Maya Saunders

10 March, 14:35

Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently supposed that if the pair (a, b) is coprime and the pair (b, c) is coprime, then the pair (a, c) is coprime. You want to find a counterexample for your friend's statement. Therefore, your task is to find three distinct numbers (a, b, c), for which the statement is false, and the numbers meet the condition l ≤ a < b < c ≤ r. More specifically, you need to find three numbers (a, b, c), such that l ≤ a < b < c ≤ r, pairs (a, b) and (b, c) are coprime, and pair (a, c) is not coprime.

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Answers (1)

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Derick · Answer 1

(5, 7, 15)

Step-by-step explanation:

A pair of numbers is coprime if the maximum number that divides the two is 1.

Consider the three numbers: 5, 7, 15

The first two numbers 5 and 7 can only be divided by 1. Hence the pair (5, 7) is coprime.

The second pair of numbers 7 and 15 is also coprime as the number which can divide both these numbers is 1. So the pair (7, 15) is also coprime

So, we have two pairs of coprime numbers: (5,7) and (7,15)

According to the friend, (5, 15) must also be coprime, but this not true as both these numbers can also be divided by 5.

Hence, the three numbers meeting the said criterion are: (5, 7, 15)