SOLUTION: What is the remainder when 1995^1993 is divided by 100?

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Question 37283: What is the remainder when 1995^1993 is divided by 100?
Answer by fractalier(6550) About Me  (Show Source):
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If you just observe the pattern of the powers of 1995, you realize that the last two digits alternate between ....25 and ....75, with .... meaning the beginning part of the number.
Since 1995^2, 1995^4, and 1995^6 all end in 25, and 1995^3, 1995^5, and 1995^7 all end in 75, it logically means that 1995^1993 ends in 75 also.
Thus dividing it by 100 leaves a remainder of 75.