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#26 2013-06-16 02:39:41

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,834
Website

Re: what is the last digit?

New Problem
Compute the last 3 digits of 171^172.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#27 2013-06-16 03:12:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: what is the last digit?

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#28 2013-06-16 03:14:54

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,848

Re: what is the last digit?

Hi Agnishom,

641


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#29 2013-06-16 04:34:57

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,834
Website

Re: what is the last digit?

I can't handle either cases.

How do you do it?

[This problem is not meant for a computer]


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#30 2013-06-16 04:37:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: what is the last digit?

I have been waiting. There are 3 basic ways.

1) Do some raising of a power and play spot the pattern.

2) Repeated squaring.

3) Use the binomial theorem.


1) Did not yield anything I could do. Which of 2 and 3 would you like?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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