Let n be a positive integer. Prove that there exists a positive integer m > 1000 with the following two properties: m's last 3 digits are 007, and m is relatively prime to n.

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Mathematics

Macie Clements

28 August, 21:59

Let n be a positive integer. Prove that there exists a positive integer m > 1000 with the following two properties: m's last 3 digits are 007, and m is relatively prime to n.

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Savion Lam · Answer 1

Answer with explanation:

We have to find two integers m and n such that, m>1000, and m's last 3 digits are 007, and n is a positive integer such that they are relatively Prime to each other.

⇒4007 is a prime number. And there can be many positive numbers prime to 4007 which are 2,3,5,7,11,13,17,19,23,29,31,37 ...

→So, Ordered pairs are = (4007,2), (4007,3), ...