jmc

Question

What is the smallest positive integer n such that n has remainder 1 when divided by 3, n has remainder 1 when divided by 4, and n has remainder 4 when divided by 5?

Accepted Answer

Since gcd(3,4) = 1, the first two requirements imply that n 112. We list the first few numbers that are 112, 13,25,37,49,...We see that 49 is the first value with remainder 4 when divided by 5.