Zeroes may occur in this puzzle, but not as the first digit of a number.

**Across**

**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.

**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.