Assume 11^10 - 1 = 0 (mod 100) (i.e. 11^10 - 1 is divisible by 100).
11^10 - 1 = 0 (mod 100)
11^10 = 1 (mod 100)
(11^2)^5 = 1 (mod 100)
(121)^5 = 1 (mod 100)
(21)^5 = 1 (mod 100) [the remainder of 121 divided by 100 is 21]
(21^2)^2(21) = 1 (mod 100)
(41)^2(21) = 1 (mod 100)
81(21) = 1 (mod 100)
1701 = 1 (mod 100)
∴ 11^10 - 1 is divisible by 100.
