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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

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

**X'(y-Xβ)=0**

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

thats the solution?

A logarithm is just a misspelled algorithm.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

(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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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

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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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

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

IPBLE: Increasing Performance By Lowering Expectations.

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