TITLE: Finding the number in the fourth corner of a square
QUESTION [5 upvotes]: If we put numbers from $1$ to $16$ in the squares without repeating in which the sum of  any rows and columns is equal  .If the numbers in  the three corners are $1,5,13$ .How to find the number in the fourth corner

REPLY [15 votes]: Let $k$ be the sum of each row and column. If $x$ is the unknown quantity in the lower right corner, then you have
$$
4 k = (1 + 2 + \dots + 16) + 1 + 5 + 13 + x = 155 + x.
$$
Now $155 \equiv -1 \pmod{4}$, so $x \equiv 1 \pmod{4}$. Now $1, 5, 13$ are already taken, thus $x = 9$.
PS And just to be on the safe side, a possible arrangement, in clockwise order starting from the top-left corner, is
$$
1, 7, 12, 16, 5, 4, 8, 15, 9, 10, 6, 3, 13, 14, 11, 2.
$$