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 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),

unpaid balance is : $149.99-$50 = $99.99 new balance = 149.99+2.62-50 = $102.61 finance charge = 99.99- 0.21/12= $1.75 new balance = 99.99+1.75 = $101.74 average daily balance method average daily balance= 3399.70/30 = $113.32 finance charge = $ 0.21/12ă—113.32 = $1.98 new balance = $149.99-50+1.98 = $101.97