$N$ is a four-digit positive integer. Dividing $N$ by $9$, the remainder is $5$. Dividing $N$ by $7$, the remainder is $3$. Dividing $N$ by $5$, the remainder is $1$. What is the smallest possible value of $N$?

Using Chinese Remainder Theorem + Modular Multiplicative Inverse, we have:

LCM[9, 7, 5]==315

N ==315m + 311, where m=0, 1, 2, 3.........etc.

When m==3, then:

N ==[315 * 3 + 311]==1,256 - the smallest 4-digit intger

That answer is wrong.