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#1 Help Me ! » GCD question » 2007-09-13 12:31:52
- mortage762
- Replies: 4
I was wondering - how would one find a solution in integers to the following equation?:
54321x + 9876y = gcd(54321, 9876)
Thanks in advance!
#2 Help Me ! » Probability question » 2007-09-13 10:27:23
- mortage762
- Replies: 1
This question was confusing me so any help would be appreciated!
Suppose that there is a tennis tournament with 32 players. Players are matched in a completely random manner, and we assume that each player always has probability 1/2 of winning a match. What is the probability that two given players meet each other during the tournament?
#3 Help Me ! » LCM and GCD Question » 2007-09-12 10:39:58
- mortage762
- Replies: 4
I had to figure out the following lcms and gcds and compare the two:
I got that
LCM(8,12)=24 and GCD(8,12)=4
LCM(20,30)=60 and GCD(20,30)=10
LCM(51,68)=204 and GCD(51,68)=17
LCM(23,18)=414 and GCD(23,18)=1
The pattern I found was that if you take the first number enclosed in the parentheses, divide it by the GCD, and multiply it by the second number in the parentheses, you get the LCM. For example, 8/4=2, which when multiplied by 12, gives you the LCM of 24.
My question is, how do I show that this relationship holds true for all m and n (where m and n are the numbers between the parentheses)?
Thanks in advance, everyone! 
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