Products sum squared

U ovom radu opisani su konkretni primjeri i rezultati vezani za produkte suma kvadrata. Kroz povijest su otkriveni identiteti koji vrijede za određeni prirodan broj \(n\) u kojima je zbroj \(n\) kvadrata pomnožen sa zbrojem \(n\) kvadrata opet zbroj \(n\) kvadrata. Proučavanjem tih produkata suma kvadrata dokazana su dva značajna teorema, Hurwitzov (1; 2; 4; 8)- teorem i Pfisterov teorem o sumama kvadrata, koji su glavna tema ovog rada. Za njihovo dokazivanje potrebni su pomoćni rezultati koji se stoga pojavljuju u radu. Također, opisane su i neke primjene tih teorema.In this thesis, specific examples and results related to the products of the sum of squares are described. Through the history, there have been discovered identities that are valid for a certain natural number \(n\) by which a sum of \(n\) squares multiplied by another sum of \(n\) squares is again a sum of \(n\) squares. By studying these products of sums of squares, two significant theorems have been proved, Hurwitz’s (1; 2; 4; 8)-theorem and Pfister’s theorem on sums of squares, which are the main topic of this thesis. To prove them, we needed auxiliary results so they therefore appear in the thesis. Moreover, some applications of these theorems are described