Find the total number of positive integer solutions of:

http://www.mathramz.com/xyz/latexren...438956f719.png

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- Jul 1st 2009, 01:37 AMdhiabPositive integer solutions
**Find the total number of positive integer solutions of:**

http://www.mathramz.com/xyz/latexren...438956f719.png - Jul 1st 2009, 01:47 AMred_dog

Then

or

Now find x and y. - Jul 2nd 2009, 12:37 AMdhiab
**Hello,Thank you,**

**Can not have :**

http://www.mathramz.com/xyz/latexren...a784fe38a8.png

BECAUSE ???????? - Jul 2nd 2009, 12:43 AMProve It
Have you tried graphing the function?

You would probably have to enter it as

.

I can see straight away that so .

Since needs to be a positive integer, we know therefore that .

Now you just need to be a perfect square. works, since , so .

See if you can come up with any other solutions... - Jul 2nd 2009, 01:51 AMdhiab
**Hello: the solutions is**

http://www.mathramz.com/xyz/latexren...c39bfaaa03.png

**In graphic of the function**http://www.mathramz.com/xyz/latexren...1c04c218bd.png ,**we find the Point****cordinates integer.**

**LOOK HERE (Evilgrin)** - Jul 2nd 2009, 01:55 AMProve It
- Jul 2nd 2009, 10:20 AMdhiab
**Hello : yes in this question**

**Hello,Thank you,**

**Can not have :**

**http://www.mathramz.com/xyz/latexren...a784fe38a8.png**

BECAUSE

AND IN THIS ANSWER :

http://www.mathramz.com/xyz/latexren...8c8e7e9f76.png - Aug 12th 2009, 03:51 AMpacman
as the graph suggests, the values are symetric, mirror image of each other,

x = -/+ 17, y = -/+ 16

x = /+ 7 ; y -/+ 4 - Aug 12th 2009, 06:57 AMSoroban
Hello, dhiab!

Here is a primitive solution . . .

Quote:

Find the number of positive integer solutions of: .

We have: .

. . Then: .

. . Hence: .

. . Hence: .

Therefore, there are exactlysolutions.*two*

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I came up with this procedure while in college.

Example: .

is the difference between and

. . Therefore: .

We have: .

. .

. . Therefore: .

We have: .

. .

. . Therefore: .

But this cannot be expressed as a sum of conscutive*positive*odd numbers.

Therefore, there are three solutions: .

- Aug 12th 2009, 10:30 AMdhiab