HELP !!!

Studying for Mathamotix Olympiad mow. Does anyone know how to prove that : ( (19^93) - (13^ 99) )/162 is a positive integer ? This sum was there in the RMO-1993 paper. I have managed to solve all the other sums, but I am not sure about the fourth question in INMO-2005 : " All possible 6-digit numbers, in each of which the digits occur in non-increasing order ( from left to right eg. 877550 ) are written as a sequence in increasing order. Find the 2005th term in this sequence. ". Now, I got the answer by creating complex AGP ( each number is found by multiplying the previous number by two, then adding an AP ) which went 1,6,21,56,132, etc. , but I cannot decide if 000000 is a part of the sequence or not. If it is, the answer will be 764322 , otherwise, 764330 ( I hope .) . HELP !!!