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PDF-ARITHMETICPROGRESSIONSOFTHREESQUARESKEITHCONRAD1.IntroductionHereareth PDF document

b2c b22soabcbisarationalpointonthecirclex2y22Converselyifxandyarerationalnumberssatisfyingx2y22writexandywithacommondenominatorasxabandycbwhereabc2ZThena2c22b2soc2b2b2a2

b2+c b2=2;so(a=b;c=b)isarationalpointonthecirclex2+y2=2.Conversely ifxandyarerationalnumberssatisfyingx2+y2=2 writexandywithacommondenominatorasx=a=bandy=c=bwherea;b;c2Z.Thena2+c2=2b2 soc2b2=b2a2

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