What is the smallest positive integer that satisfies the congruence \(30x \equiv 42 \pmod{47}\)?
30x = 42 (mod 47)
30x = 47n + 42. n is an integer.
6(5x - 7) = 47n. 47 is prime so n must be a multiple of 6
n. 5x
1*6. 54. Not divisible by 5
2*6. 101. Not divisible by 5
3*6. 148. Not divisible by 5
4*6. 195. So x = 195/5.
x = 39
+249 
