ACROSS: A: square of C down
G: the third power of the sum of A across's digits
H: divisible by the sum of G across's digits
I: divisible by digit sum of C down
J: I across + digit sum of I across
K: a square number
L: the reverse of M down
M: I across multiplied with the digit sum of H across
N: every digit (except for the last one) is smaller than the subsequent digit.

DOWN: A: the reverse of C down multiplied with E down
B: a palindrome
C: a prime number
D: the reverse of D down equals A across + F down
E: the digit sum of A across
F: the third power of the reverse of E down
K: a prime number
L: yet another prime number
M: the reverse of L across