Solution: ∫a is a "hope number". According to the definition of "hope number", there is a natural number p rearranged by the number of a, so that a=3p and the sum of the numbers of a equals the sum of the numbers of p. 。

∫A = 3p, A is a multiple of 3, but the sum of the numbers of A is equal to the sum of the numbers of P,

From the divisible discrimination method, we know that p is a multiple of 3.

∴p=3m, (m is a positive integer),

∴a=3×p=3×3m=9m，

∴a is divisible by 9.

The sum of the numbers of ∫A is equal to the sum of the numbers of P,

∴ According to the discrimination method of divisibility by 9, p can be divisible by 9, that is, p=9k(k is an integer).

∴p=3a=3×9k=27k

∴a is a multiple of 27.

∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴875

∫a and B are both "hope numbers",

∴a and B are multiples of 27, that is, a=27n 1 and b=27n2(n 1, n2 is a positive integer).

∴ab=(27n 1)(27n2)

=(27×27)(n 1×n2)

=729n 1n2。

∴ab must be a multiple of 729.