Zeroes may occur in this puzzle, but not as the first digit of a number.
A: V down + Y across.
D: D across is a multiple of Y down.
I: I across equals the first digit of I across multiplied with W down.
J: J across is a multiple of V across.
K: a prime number.
L: a multiple of U across.
M: A' across minus D down minus the digit sum of S down.
N: the first digit of N across multiplied with the reverse of R across.
P: has the same digit sum as W across.
Q: a prime number.
R: a prime number.
T: has the same digit sum as W down.
U: a multiple of the digit sum of B down.
V: divide Y across by the sum of the digit sum of A down and the digit sum of T across, and the result is a divisor of V across.
W: a multiple of the average of the digit sums of K across and T across.
X: a palindrome and prime number.
Y: a multiple of the sum of A down's and T across's digit sums.
Z: a cubic number.
A': D down + M across + the digit sum of S down.
A: a multiple of F down.
B: I across + 1.
C: the digit sum of C down equals Y down.
D: the reverse of S down multiplied with V down.
E: the fourth power of K across.
F: to get F down, multiply G down with T across and subtract this result from E down.
G: The digit sum of G down is a square number.
H: has the same digit sum as S down.
J: a palindrome.
L: a palindrome.
M: a prime number.
O: a multiple of the digit sum of G down.
R: a multiple of R across.
S: a prime number.
U: the reverse of the sum of V down and S down.
V: multiply all digits of S down. Take this digit product, and again, multiply all of its digits. The result is a divisor of V down.
W: the digit product of Z across.
X: the reverse of X across.
Y: a palindrome.
Z: a square number.