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From: simon@bowfin.cs.washington.edu (Kevin Simonson)
Newsgroups: comp.edu,sci.math,sci.misc,ut.general,uw.general,uw.math.grad,york.general
Subject: Re: Subtle Math Questions
Summary: 5 to the 7777th power
Message-ID: <1991Apr23.163231.27780@beaver.cs.washington.edu>
Date: 23 Apr 91 16:32:31 GMT
References: <2729@ttardis.UUCP> <1991Apr22.165415.9843@contact.uucp> <1991Apr22.235606.10856@ms.uky.edu>
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Reply-To: simon@cs.washington.edu (Kevin Simonson)
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     In article <1991Apr22.235606.10856@ms.uky.edu> ghot@ms.uky.edu (Allan
Adler) writes:

=
=Now that Roy Wood has explained that he has no hidden agenda, I would
=like to contribute some "subtle" questions off the top of my head.
=
=
=
=(1) ...
=(6) What are the last 4 digits of 5 to the 7777th power ?
=    (YOu are not allowed to use a calculator. Anyone who uses a
=    calculator will be expelled, their reputation tarnished, their
=    future ruined and their children left to fend for themselves
=    in a cold and hostile world.)

     Allan, I REALLY didn't use a calculator for this.

     For all i > 0 5^(4i) mod 10000 = 625.  7777 = 4*1944 + 1, so

5^7777 mod 10000 = 5^(4*1944+1) mod 10000 = 5(5^(4*1944)) mod 10000
                 = 5*625 = 3125.

     Somebody with a calculator might want to check me on this.

                                      ---Kevin Simonson