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 Post subject: Finding the remainderPosted: Fri, 10 Aug 2012 23:22:44 UTC
 Senior Member

Joined: Mon, 10 Mar 2008 04:43:48 UTC
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What is the remainder of ?

How do I solve this problem?

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 Post subject: Re: Finding the remainderPosted: Fri, 10 Aug 2012 23:23:29 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
johndoe wrote:
What is the remainder of ?

How do I solve this problem?

Use modular arithmetic. The order of 3 mod 5 is 4.

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 Post subject: Re: Finding the remainderPosted: Fri, 10 Aug 2012 23:45:45 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
If you are not familiar with "mod" stuff, find the remainder of
, etc.
and see if you notice a pattern.

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 Post subject: Re: Finding the remainderPosted: Fri, 10 Aug 2012 23:47:34 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
alstat wrote:
If you are not familiar with "mod" stuff, find the remainder of
, etc.
and see if you notice a pattern.

If he's not familiar with it whoever asked him this question should have his head examined.

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 Post subject: Re: Finding the remainderPosted: Sat, 11 Aug 2012 03:56:08 UTC
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Joined: Mon, 10 Mar 2008 04:43:48 UTC
Posts: 113
Location: Autistic nation
alstat wrote:
If you are not familiar with "mod" stuff, find the remainder of
, etc.
and see if you notice a pattern.

the remainder squence goes as 3,4,2,1

so for the 58th power, the remainder is 4

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 Post subject: Re: Finding the remainderPosted: Sat, 11 Aug 2012 08:21:21 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
If he's not familiar with it whoever asked him this question should have his head examined.

Not necessarily - I see problems like this all the time in math competitions for high school and even junior high students. Although the solution requires the basic ideas of modular arithmetic, I know I could have solved it many years before I ever even heard of "mod 5." One can use concepts before learning what they are called.

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 Post subject: Re: Finding the remainderPosted: Sun, 12 Aug 2012 08:04:52 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
alstat wrote:
If he's not familiar with it whoever asked him this question should have his head examined.

Not necessarily - I see problems like this all the time in math competitions for high school and even junior high students. Although the solution requires the basic ideas of modular arithmetic, I know I could have solved it many years before I ever even heard of "mod 5." One can use concepts before learning what they are called.

There are obviously exceptions, but it's not an unreasonable thing to say either.

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