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If a and m are positive integers, then what is the remainder of a^m/3?

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If a and m are positive integers, then what is the remainder of a^m/3?  [#permalink]

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New post 29 Jun 2018, 04:38
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:57) correct 42% (01:27) wrong based on 62 sessions

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If a and m are positive integers, then what is the remainder of a^m/3?  [#permalink]

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New post Updated on: 29 Jun 2018, 08:58
1
Bunuel wrote:
If a and m are positive integers, then what is the remainder of a^m/3 ?

(1) m is even.
(2) a is prime number greater than 9.


Ans: C
when finding the remndr of (a^m)/3 we need to know values of a and m
from stat-1: m is even : here a can be anything.
when a=2 m=2 then 4/3 remndr is 1; when a = 3 m=2 then 9/3 remndr is 0 (Not sufficient)

from stat: 2: a is a prime number greater than 9
so a can be 11, 17, 19 lest put the values
a=11 m=1, 11/3= remndr is 2
m= 2, a = 11^2= 121 remndr is 1 (not sufficient)

after getting correction of my mistake:
Thank you bhatiabhavya
Edited:
both together: a= 11 and m=2 then 121/3 reminder is 1,
a=17 m=2 then 289/3 remndr is 1
a=43 m=2 then 1849/3= remndr is 1
a=101 m-2 then 10201/3 = remndr is 1
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Originally posted by D3N0 on 29 Jun 2018, 05:07.
Last edited by D3N0 on 29 Jun 2018, 08:58, edited 1 time in total.
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Re: If a and m are positive integers, then what is the remainder of a^m/3?  [#permalink]

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New post 29 Jun 2018, 07:55
I'm not sure if it's e. Could be c. Can you give more proof? If you take them together, then:
11^2 remainder is 1
17^2 remainder is 1
19^2 remainder is 1
23^2 remainder is 1
83^2 remainder is 1

Give one proof where remainder isn't 1 when m is even?

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Re: If a and m are positive integers, then what is the remainder of a^m/3?  [#permalink]

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New post 29 Jun 2018, 07:56
Btw, 17^2 = 289 dude.289/3 remainder is 1.

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Re: If a and m are positive integers, then what is the remainder of a^m/3?  [#permalink]

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New post 29 Jun 2018, 08:47
bhatiabhavya wrote:
Btw, 17^2 = 289 dude.289/3 remainder is 1.

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That's where i made mistake... :)
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Re: If a and m are positive integers, then what is the remainder of a^m/3? &nbs [#permalink] 29 Jun 2018, 08:47
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