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2a which represent 2aki assume b'xy basis ui binary quadratic form bx'y class of forms class of ideals class of left classes of hermitian co's complex integers conjugate contains no square Dickson discriminant 2a division algebra equivalent to 8i F represents f's form factorization of elements form a proper form corresponding form of determinant form with leading forms ax2 Hence hermitian forms Hurwitz integral ideal is equivalent ideals containing indefinite primitive integral elements integral quaternions JAMES H. D. TELLER JV(ft KENTUCKY Latimer Latimer's leading coefficient left ideals left member LEMMA Multiplying the left number odd prime odd rational integer phrase non-singular prime factor primitive indefinite form principal ideal proper basis ft prove THEOREM QUATERNION ALGEBRAS range over G rational prime represent positive integers represents a positive shown square factors ternary form uniquely determined unit left factor