- Hello! TO ALL!

Any one my Brother who help me about the

solution of the following linear Diophantine

equations, I am very worried about that, so if anyone

who want to help me please send me the solution via

attachment of Scanned Document, or MS-Word attachment,

or any mean. This is my request to All of U!

These Exercises about the solution "LINEAR DIOPHANTINE

EQUATION"

ExERCISE: Find the general solution for the following

equation:

1. 252x + 580y =20

2. 85x + 34y =51

3. 85x + 34y =53

4. 8x + 10y =42

5. 321x + 105y =1

6. 31x - 7y =2

7. 45x + 63y =450

8. 170x - 455y =625

EXERCISE: Find positive solution of the following

simultaneous linear diophantine eqution:

7x + 11y + 13z = 125

3x + 4y + 5z = 48

Bye! TAKE CARE!

YOUR TRUELY,

Muhammad Idrees.

__________________________________________________

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

http://mail.yahoo.com - Hello Muhammad

This group is not an apropriate place for solving your homework problems.

You can use Yahoo Answers instead.

Payam

On 2/9/06, Muhammad Idrees <idrees1000@...> wrote:

>

> Hello! TO ALL!

> Any one my Brother who help me about the

> solution of the following linear Diophantine

> equations, I am very worried about that, so if anyone

> who want to help me please send me the solution via

> attachment of Scanned Document, or MS-Word attachment,

> or any mean. This is my request to All of U!

>

>

>

> These Exercises about the solution "LINEAR DIOPHANTINE

> EQUATION"

>

> ExERCISE: Find the general solution for the following

> equation:

>

> 1. 252x + 580y =20

>

> 2. 85x + 34y =51

>

> 3. 85x + 34y =53

>

> 4. 8x + 10y =42

>

> 5. 321x + 105y =1

>

> 6. 31x - 7y =2

>

> 7. 45x + 63y =450

>

> 8. 170x - 455y =625

>

>

> EXERCISE: Find positive solution of the following

> simultaneous linear diophantine eqution:

> 7x + 11y + 13z = 125

> 3x + 4y + 5z = 48

>

>

> Bye! TAKE CARE!

> YOUR TRUELY,

> Muhammad Idrees.

>

[Non-text portions of this message have been removed] - In an attempt to make something on-topic out of this...

EXERCISE: Consider the diophantine equations:

7x + 11y + 13z = 125

3x + 4y + 5z = 48

Note that a particularly pretty solution is:

(x,y,z) = (-3001, -4001, 5011)

And that 3001, 4001, and 5011 are all twin primes. :) - Hello,

I agree with you Jack

I believe that we need a definition of "pretty"

though.

Perhaps a prime can be called pretty when there are

long strings of the same digit in its decimal

representation?

Pavlos

--- jbrennen <jb@...> wrote:

> In an attempt to make something on-topic out of

__________________________________________________

> this...

>

> EXERCISE: Consider the diophantine equations:

> 7x + 11y + 13z = 125

> 3x + 4y + 5z = 48

>

> Note that a particularly pretty solution is:

>

> (x,y,z) = (-3001, -4001, 5011)

>

> And that 3001, 4001, and 5011 are all twin primes.

> :)

>

>

>

>

>

>

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

http://mail.yahoo.com - Speaking of pretty, here is a different kind of pretty:

1+2*3^4 = 163 is prime. (Just looked and it's in Prime Curios!)

2^(2^2^2-1) + (2^2^2-1)^2 = 32993 is prime. (Also in Prime Curios!)

(3^4-1)^(3^4) + (3^4)^(3^4-1) is a 155 digit prime.

(7^3-1)^(7^3) + (7^3)^(7^3-1) is a 870 digit prime.

(Proven by Paul Leyland, see

http://groups.yahoo.com/group/primenumbers/message/1263 )

On a different note,

n^(n+1) - (n+1)^n is prime for n=3,6,9,12, and ... 44.

(Up to 100. Hehe, I no longer expect primes to yield a pattern for

very long. )

n^(n+1) + (n+1)^n is prime for n = 3^(1^2)-1 and n=3^(2^2)-1.

Hoping against hope, might it be prime for

n=3^(3^2)-1 or perhaps

n=3^(3^3)-1 or perhaps

n=3^(2^4)-1 or ?

(Don't know, goes too high for what I have.)

Mark

--- In primenumbers@yahoogroups.com, Pavlos S <pavlos199@...> wrote:

>

> Hello,

> I agree with you Jack

> I believe that we need a definition of "pretty"

> though.

>

> Perhaps a prime can be called pretty when there are

> long strings of the same digit in its decimal

> representation?

>