Homepage Solution manuals Ivan Niven An Introduction to the Theory of Numbers Exercise 2.3.12 (Number of positive integers $n\leq 7200$ prime to $3600$.)

Exercise 2.3.12 (Number of positive integers $n\leq 7200$ prime to $3600$.)

Find the number of positive integers 7200 that are prime to 3600 .

Answers

Proof. Since k 3600 = 1 is equivalent to ( 3600 + k ) 3600 = 1 , there are as many integers prime with 3600 in [ [ 1 , 3600 ] ] than in [ [ 3601 , 7200 ] ] . Therefore, the number N 2 of positive integers n 7200 that are prime to 3600 is

N 2 = 2 ϕ ( 3600 ) = 2 × 960 = 1920 .

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2024-08-11 17:30
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