8^100 is divisible by 17. Find the remainder?	Pick one
A) 8  B) 12  C) 16  D) 18  E) 20
This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.   So divide 100 by 16 and find the remainder. Remainder = 4   Therefore, 100 = (16 × 6) + 4   Now this problem can be written as 810017 = 816×6+417 = (816)6×8417   Now this problem simply boils down to (1)6×8417 = 8417   84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.   16
<result>C</result>
8^100 is divisible by 17. Find the remainder?