Question

Find in set builder notation the set of all positive integers a such that
a≡137 (mod 5).

Answer 1

137≡2(mod5)

 so we need all positive integers that are 2 more than a multiple of 5. Any positive integer which is 2 more than a multiple of 5 can be written as 

a=5n+2 for n∈N (where the natural numbers are taken to be 0,1,2,...). So we have {5n+2|n∈N}