Note that 6 divides both $30x$ and $42$, and since 6 is relatively prime to 47, we can write $5x \equiv 7 \pmod{47}$. Note that $5 \cdot 19 = 95 = 2(47) + 1$, so 19 is the modular inverse of 5, modulo 47. We multiply both sides of the given congruence by 19 to obtain $95x \equiv 19(7) \pmod{47}\implies x \equiv \boxed{39} \pmod{47}$.
What is the smallest positive integer that satisfies the congruence $30x \equiv 42 \pmod{47}$?
{'answer': '39', 'subject': 'Number Theory', 'level': 4, 'unique_id': 'test/number_theory/64.json'}