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What are the last two digits of (1+5^(2n+1))/6?

Note that n is assumed to be any positive integer.

Source: The current issue ofCrux(Problem 2578).© Copyright 2000 Stan Wagon. Reproduced with permission.

NOTE:This is from the Problem Section ofCrux. It is our hope that one of the Macalester Students will solve the problem and send in a solution by the deadline of April 1. We will not post a solution to the email list or on the web site until then.

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7 December 2000