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Solving question (1 Viewer)

cutemouse

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Find 6 integer solutions for x and y such that:

x2+2009=y2
 

Aquawhite

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That's a really good problem solving question. I personally don't know how to solve it, but I'd like to see some others give it a go.
 

Iruka

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Re-write as

y^2-x^2=2009

Factorise using difference of 2 squares:

(y-x)(y+x) =2009

If x and y are both integers, then so are y-x and y+x.

Find the prime factorisation of 2009 and then check what all the possibilities for x and y are.
 

Iruka

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Doing that I got:

y= +/- 1005, x=+/-1004

y= +/- 147, x=+/-140

y= +/- 45, x=+/-4
 

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