- #1

- 61

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all odd integers ,(2n+1) where n≥0, are representable by the

*difference*of TWO squares

[1= 1[SUP]2[/SUP] -0

^{2}]

so 3 = 2

^{2}-1

^{2}

5 = 3

^{2}-2

^{2}

7 = 4

^{2}-3

^{2}

and generally,

Z =y

^{2}-x

^{2}

and Z + x

^{2}= y

^{2}where y= Z/2 +1/2

[even integers of the form 4n are representable where y=Z/4+1 and x=y-2]

is there a term, in English language, to describe the x

^{2}mathematical term

that ,when added to Z, forms a perfect square, y

^{2}?

Thanks to anyone who will give me a definitive answer - I feel it should start with

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