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# The remainder when 7^84 is divided by 342 is:

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CEO
Joined: 15 Aug 2003
Posts: 3454
The remainder when 7^84 is divided by 342 is: [#permalink]

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14 Sep 2003, 05:54
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The remainder when 7^84 is divided by 342 is:

A. 0
B. 1
C. 49
D. 341
Intern
Joined: 12 Sep 2003
Posts: 31
Location: Peru

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14 Sep 2003, 21:48
7^84 = 7^2 * 7^2 * 7^2.........(42 times)

Numbers ending in 9 powered end either in 9 or in 1; so, both of them divided by a number ending in 2, produce a remaining of 1
Intern
Joined: 28 Aug 2003
Posts: 36
Location: USA

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14 Sep 2003, 22:28
praetorian123 wrote:
The remainder when 7^84 is divided by 342 is :

1. 0
2. 1
3. 49
4. 341

7^3 = 343. So, 7^84 can be written as 243^28. And write that number as (242 + 1)^28. If we expand that expression, all terms will be multiples of 242 except 1^28 (which is 1). So, remainder is 1.
Re: PS : Remainder   [#permalink] 14 Sep 2003, 22:28
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