Across
A: A prime number.
C: This palindrome equals twice B down
E: D down / reverse(I across)
G: Twice C across.
I: P across * A across / L across
J: Divide G down by J across, and the result is a palindrome.
K: the reverse of a square number
L: F down / I across
M: A square number.
N: C down divided by the reverse of J across
O: P across - J across
P: P across equals 2 ^ (L across / A across). Also, the digit product of D down equals twice P across.
Q: This palindrome equals four times the reverse of K across.

Down
B: a palindrome.
C: All digits are the same.
D: E across times the reverse of I across
E: L across * M across
F: F down / P across = A across
G: The first two digits are repeated in the last two digits (1st digit = 4th digit, 2nd digit = 5th digit)
H: 2 * D down
K: Q across + P across