Question 459304
According to the Chinese remainder theorem, there must exist an integer and all such solutions are congruent modulo 60. Since adding 60 will not change the residue of each of the three cases (3, 4, 5), we now know that the smallest possible positive integer that satisfies is less than 60. I just used trial and error and got 58 as the smallest possible integer. We can also see that 118, 178, ... satisfy as well.