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## #1 2006-04-06 02:28:15

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

### a b + c d = 6 && a c - 3 b d = 5

Find all integer solutions of the system:
a b + c d = 6 && a c - 3b d = 5.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #2 2006-04-06 13:16:56

George,Y
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Registered: 2006-03-12
Posts: 1,306

### Re: a b + c d = 6 && a c - 3 b d = 5

(a+d)(b+c) = 6+5+4bd

X'(y-Xβ)=0

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## #3 2006-04-06 14:02:30

mikau
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Registered: 2005-08-22
Posts: 1,504

### Re: a b + c d = 6 && a c - 3 b d = 5

thats the solution?

A logarithm is just a misspelled algorithm.

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## #4 2006-04-06 20:18:09

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

### Re: a b + c d = 6 && a c - 3 b d = 5

:0
No. You haveto find all fours (a0,b0,c0,d0) elem Z:
a0 b0 + c0 d0 = 6 && a0 c0 - 3 b0 d0 = 5

IPBLE:  Increasing Performance By Lowering Expectations.

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## #5 2006-04-07 03:13:47

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

### Re: a b + c d = 6 && a c - 3 b d = 5

(a+d)(b+c) = 6+5+4bd
contains all the information of a b + c d = 6 and a c - 3b d = 5. and it might be a path. i'm new in this field, and what i could do is shifting, to see if it has been made simplier....

Last edited by George,Y (2006-04-07 03:15:54)

X'(y-Xβ)=0

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## #6 2006-04-07 05:33:42

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: a b + c d = 6 && a c - 3 b d = 5

You are not so right:
{a b + c d = 6 && a c - 3b d = 5} => {(a+d)(b+c) = 11+4bd}, but:
{a b + c d = 6 && a c - 3b d = 5} !<=> {(a+d)(b+c) = 11+4bd}, so not all solutions of your equation will be solutions to the system.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #7 2006-04-07 20:07:00

George,Y
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Registered: 2006-03-12
Posts: 1,306

### Re: a b + c d = 6 && a c - 3 b d = 5

yes, you'r right. sufficient but not necessary. at least one of the original equation have to be contained.
from  a c - 3b d = 5, ac-5 contain 3 , ac  elem {8,11,14...}

X'(y-Xβ)=0

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## #8 2006-04-08 22:10:24

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

### Re: a b + c d = 6 && a c - 3 b d = 5

a c elem {...8,11,14,...}:: a IS integer

IPBLE:  Increasing Performance By Lowering Expectations.

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