Two consecutive odd numbers can be expressed as 2n- 1 and 2n+ 1(n is a positive integer).

Then the password must be:

(2n+ 1)^2-(2n- 1)^2

=8n

So the secret number is a multiple of 8.

1)2003÷8=250……3

So the minimum number that meets the conditions is

8×25 1=2008

2) Two consecutive even numbers can be represented as 2n and 2n+2.

(n is a positive integer)

(2n+2)^2-(2n)^2

=8n+4

It is not a multiple of 8, so it is not a secret number.