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# Linear Diophantine Equations

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x,y,z are three consecutive positive odd integers that satisfy y^2 - x^2 = 344. Find the value of z?

Work done:

(y+z) (y-z) = 344

(y+z) = 43

(y-z) = 4

y=4+z

y+z = 86

4+z+z = 86

2z = 82

z = 41

Where did I mess up? Says the answer is 89...? (didn't know the other way to say nail was censored, sorry!)

Jan 1, 2021
edited by TheOddOne  Jan 1, 2021

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Hello TheOddOne (I love your profile picture)

The formula you used is x^2 - y^2 = (x+y)(x-y)

So  y^2 - x^2 = 344 is actually (y+x)(y-x) = 344.

Since x = y + 2.

Following your logic, y - x = 2 (consecutive odd number), so y + x = 172 (344/2).

y = 85

x = 87

Which makes z 89.

I hope this helped. :)))

=^._.^=

Jan 1, 2021
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Hi catmg!

So if I'm reading this right:

( y - x ) = 2

( y + x ) = 172

- x = 2 - y

x = y - 2

Where did you get y+2?

Did I make another addition mistake... I shouldn't stay up late lol

TheOddOne  Jan 1, 2021
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Also, I kept flipping x and z. My fault... It's all supposed to be x so far. The question is what is z?

TheOddOne  Jan 1, 2021
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People cannot make sense of it if you cannot get your x's and y's in the right places.

Neither of us know what the question in your head is.... Well I do not anyway.

Melody  Jan 1, 2021
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Hello TheOddOne again

I think I have a better sense of the problem now.

Consecutive odd number are like 1, 3, and 5 or 7, 9, 11.

They are odd numbers that are right next to each other.

Another way to write them is x, x+2, x+4, when x is an odd number.

If x, y, and z are consecutive odd numbers then y = x + 2 and z = x + 4.

Do you have anymore questions?

But next time, try to be a bit more careful when writing variables, it can get a bit confusing.

=^._.^=

catmg  Jan 1, 2021
edited by catmg  Jan 1, 2021
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I don't know how to reedit the question, which I would have if I could. It won't let me.

TheOddOne  Jan 1, 2021
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Oh, can I ask again in a bit? I think I got it.

TheOddOne  Jan 1, 2021
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That's amazing. :)))

I love the feeling of finally understanding a problem.

=^._.^=

catmg  Jan 1, 2021
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Happy new years!

wolfiechan  Jan 1, 2021
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Dont feel bad everyone makes mistakes!

wolfiechan  Jan 2, 2021
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Yes,  you can repost it properly if you want.  Make sure you proofread the new question very carefully.

Jan 2, 2021
edited by Melody  Jan 2, 2021