Page:Joseph Louis de Lagrange - Œuvres, Tome 3.djvu/770

TABLE V.

Formule des nombres proposés $\ldots t^{2}+au^{2}.$

Formule des non-diviseurs $\ldots 4an+b.$

${\begin{array}{|c|c|}\hline \\\scriptstyle {\mathrm {VALEURS\ DE} }&\,\quad \qquad \qquad \scriptstyle {\mathrm {VALEURS\ CORRESPONDANTES\ DE} }\,\quad \qquad \qquad \\a&b\end{array}}$

${\begin{array}{|l|}&{\begin{array}{c|l}\hline \\\ \ \quad 1\quad \ \ &-1\\2&-1,-3\\3&\quad 5,-1\\5&-1,-3,-7,-9\\6&-1,-5,7,-11\\7&\quad 3,5,13,-1,-9,-11\\10&\quad 3,17,-1,-9,-11,-13,-19\\11&\quad 7,13,17,19,21,-1,-3,-5,-9,-15\qquad \qquad \qquad \end{array}}\\&{\begin{array}{cl|l}\quad 13\ \ \,&\left\{{\begin{array}{l}&3,5,21,23,-1,-7,-9,-11,-15,-17,\\&\quad -19,-25\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 14\ \ \,&\left\{{\begin{array}{l}&11,17,-1,-3,-5,-9,-13,-15,-19,-23,\\&\quad -25,-27\end{array}}\right.\\\end{array}}\\&{\begin{array}{c|l}\quad 15\quad \ \ &\quad 7,11,13,29,-1,-17,-19,-23\end{array}}\\&{\begin{array}{cl|l}\quad 17\ \ \,&\left\{{\begin{array}{l}&5,15,19,29,-1,-3,-7,-9,-11,-13,-21,\\&\quad -23,-25,-27,-31,-33\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 19\ \ \,&\left\{{\begin{array}{l}&3,13,15,21,27,29,31,33,37,-1,-5,-7,-9\\&\quad -11,-17,-23,-25,-35\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 21\ \ \,&\left\{{\begin{array}{l}&13,29,-1,-5,-11,-17,-19,-23,-25,-31,\\&\quad -37,-41\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 22\ \ \,&\left\{{\begin{array}{l}&3,5,7,17,27,37,39,41,-1,-9,-13,-15,\\&\quad -19,-21,-23,-25,-29,-31,-35,-43\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 23\ \ \,&\left\{{\begin{array}{l}&5,7,11,15,17,19,21,33,37,43,45,-1,-3,-9,\\&\quad -13,-25,-27,-29,-31,-35,-39,-41\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 26\ \ \,&\left\{{\begin{array}{l}&11,19,23,29,33,41,-1,-3,-5,-7,-9,-15,\\&\quad -17,-21,-25,-27,-31,-35,-37,-43,\\&\quad -45,-47,-49\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 29\ \ \,&\left\{{\begin{array}{l}&7,17,21,23,35,37,41,51,-1,-3,-5,-9,-11,\\&\quad -13,-15,-19,-25,-27,-31,-33,-39,\\&\quad -43,-45,-47,-49,-53,-55,-57\end{array}}\right.\\\end{array}}\\&{\begin{array}{cl|l}\quad 30\ \ \,&\left\{{\begin{array}{l}&7,19,41,53,-1,-11,-13,-17,-23,-29,\\&\quad -31,-37,-43,-47,-49,-59\end{array}}\right.\\\end{array}}\\&{\begin{array}{c|l}\qquad \quad \ \ &\end{array}}\\\hline \end{array}}$