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# What is the gcd of (2^a) - 1 and (2^b) -1 1. gcd(a, b) = 3

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What is the gcd of (2^a) - 1 and (2^b) -1 1. gcd(a, b) = 3 [#permalink]

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12 Apr 2004, 12:19
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What is the gcd of (2^a) - 1 and (2^b) -1

1. gcd(a, b) = 3
2. lcm(a, b) = 9

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CEO
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22 May 2004, 04:43
no one tried to solve this?

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SVP
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22 May 2004, 10:30
a) gcd(a,b) = 3 this is satisfied by (3,6) and (3,9)
gcd of (2^a) - 1 and (2^b) -1 is ether 7 or 1
Insufficient

b) lcm(a,b) = 9 this is satisfied by (1,9), (3,9)
gcd of (2^a) - 1 and (2^b) -1 is 1

So B is sufficient.

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26 May 2004, 20:21
anandnk wrote:
a) gcd(a,b) = 3 this is satisfied by (3,6) and (3,9)
gcd of (2^a) - 1 and (2^b) -1 is ether 7 or 1
Insufficient

b) lcm(a,b) = 9 this is satisfied by (1,9), (3,9)
gcd of (2^a) - 1 and (2^b) -1 is 1

So B is sufficient.

Anandnk,
i'm having a brain freeze, what does lcm and gcd stand for and how is it used in this example?
merci!

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26 May 2004, 21:04
lcm - least common multiple

take two numbers 12 and 3 what is smallest number that is divisible by both these numbers? I guess 12

gcd - greatest common divisor

take two numbers 12 and 3 what is the biggest number that can divide both of these ? I guess 3

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27 May 2004, 05:57
Hmm anandnk, I don't think I agree with your answer. I think the answer should be C.

Quote:
What is the gcd of (2^a) - 1 and (2^b) -1

1. gcd(a, b) = 3
2. lcm(a, b) = 9

1) Insufficient. We only know that a and b have 3 in common. a could be greater than or less than b.

2) Also insufficient.
If a = 3^2 and b= 3, LCM = 3^2, then the gcd of (2^9) - 1 and (2^3) - 1 is 7.

If a = 3^2 and b = 3^2, LCM = 3^2, then the gcd of (2^9) - 1 and
(2^9) - 1 is 511.

Together,
Either a = 3^2 and b = 3 OR a = 3 and b = 3^2. Regardless, the gcd(a,b) will be 7 so the answer should be C. Both statements are sufficient together.

Last edited by Makky07 on 27 May 2004, 07:09, edited 1 time in total.

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27 May 2004, 07:07
Yeah did a silly mistake. I though 511 was a prime number.

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27 May 2004, 13:45

gcd(x^m - y^m, x^n - y^n) = x^k - y^k, where k = gcd(m, n)

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27 May 2004, 13:45
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