We are given: .
Equate  and : .
. . . Multiply by 35: .
. . . . . . . . .Factor: .
Hence, the only integer values of are: .
. . Therefore: .
An integer has the properties that and for some integer , what is ?
My solution is as follows:
Let and and , where and . Then
Let be a set of relation defined by . We find the integer , and the result is
Remark: The solution involved repeating input of integer until and have a common divisor greater than 2, which doesn't seem very mathematical.
1. Could anyone show me a better solution?
2. Is it possible to solve this using the Euclidean Algorithm?