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2-ic partitions algebraic factors Aurifeuillian condition 45 Aurifeuillian Factors Aurifeuillians of order Aurifn Base-form Bin-Aurifn CM CM CM co-factors conformal division Congruence-Tables Congruences difference of squares Dimorphs divisors expressed algebraically factorisation Factorisation-Tables formulae given H. J. Woodall Hereby the impure i-nO impure 2-ic form inco inno inoo involves—under iOCO Least Boots Linear form llu2 lOnO lOSO n i n N N N N N N N O n O n n-ans NNNNN Nxxv1 Nxxx1x OnCO Onno onoo ordinary pure forms prime factors process of conformal pure 2-ic forms Quotient Quotient-Aurifeuillian Quotient-forms reduced roots simply changing Sub-Simple Tables Tf Tf Tf TfCO three impure forms three pure TJ-CO tOCO tono tooo tOSO Tredecimans tsCO Undecimans