Rupesh, after what you got in equation (1), you can easily conclude that the given number, that is, 2222^5555 + 5555^2222 is divisible by 7.

Here is the reason why:

5^1111 + 2^1111 ----------------------- Eqn 1

This was your equation (1). Now we know that a^n + b^n is divisible by a + b whenever n is odd, which implies 5^1111 + 2^1111 is divisible by 7, which again in turn implies that 2222^5555 + 5555^2222 is divisible by 7.

That solves our problem. :)

Posted by Ravi Raja on 2005-05-25 06:05:19