Question

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.

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),..........