Finding the remainder

johndoe · **Posted:** Fri, 10 Aug 2012 23:22:44 UTC

What is the remainder of $3^{58} \div 5$ ?

How do I solve this problem?

Shadow · **Posted:** Fri, 10 Aug 2012 23:23:29 UTC

johndoe wrote:

What is the remainder of $3^{58} \div 5$ ?

How do I solve this problem?

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

alstat · **Posted:** Fri, 10 Aug 2012 23:45:45 UTC

If you are not familiar with "mod" stuff, find the remainder of
$3^1 \div 5, 3^2 \div 5, 3^3 \div 5$ , etc.
and see if you notice a pattern.

Shadow · **Posted:** Fri, 10 Aug 2012 23:47:34 UTC

alstat wrote:

If you are not familiar with "mod" stuff, find the remainder of
$3^1 \div 5, 3^2 \div 5, 3^3 \div 5$ , 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.

johndoe · **Posted:** Sat, 11 Aug 2012 03:56:08 UTC

alstat wrote:

If you are not familiar with "mod" stuff, find the remainder of
$3^1 \div 5, 3^2 \div 5, 3^3 \div 5$ , 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

alstat · **Posted:** Sat, 11 Aug 2012 08:21:21 UTC

Shadow 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.

Shadow · **Posted:** Sun, 12 Aug 2012 08:04:52 UTC

alstat wrote:

Shadow 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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Finding the remainder

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