Discussion

If an integer n is divided by 7, the remainder is 3. What will be the remainder if 5n is divided by 7?

Answer: B

We are given that \(n \equiv 3 \pmod{7}\). We want to find the remainder of 5n when divided by 7. We can multiply the remainder by 5: \(5n \equiv 5 \times 3 \pmod{7} \equiv 15 \pmod{7}\). Now we find the remainder of 15 when divided by 7. \(15 = 2 \times 7 + 1\). The remainder is 1.