800 



SUBJECT INDEX. 



Denumerant, 123, 134-5 



Derivatives of Arbogast, 120, 

 129, 133, 158 



Descent, indefinite, 228, 256, 

 276, 353, 465, 533, 546, 

 548, 550, 574, 576, 615-9, 

 632, 634, 636-8, 738, 748 



Determinant, 75, 76, 82-84, 

 89-93, 95, 121, 125, 244, 

 291, 314, 416, 556, 594, 679, 

 689, 695, 741-2, 756 



Diagonal number, 342 



Diametral number, 167, 170, 

 342 



Difference of 2 squares, 402- 

 5, 420, 426, 535, 549 



biquadrates not a 



square, 615-20 



Differences of order n, 13, 14, 

 15, 117, 124, 231-2, 366 



three squares, 446, 450, 



452, 454, 505 



- two biquadrates, pro- 

 duct of two, equal to third, 

 470 



a square 



505 

 cubes, 535, 549, 578- 



581, 607, 662 

 Differential operator, 134, 



154, 162 

 Digits, 20, 27, 33, 38, 52, 138, 



166, 309, 310, 379, 459, 



685, 699 



Discordant forms, 473 

 Discriminant of cubic, 548, 



595, 662, 736 



- equal unity, 695-6 

 Distributions, 145, 162-3 

 Divisor with odd conjugate, 



130 



- product, 701 

 Divulsions, 101 

 Dodecahedral, 16, 23 

 Double equalities, 80, 443, 445 



Elementary divisor, 83, 90 

 Elliptic function, 25, 113, 146, 

 209, 220, 224, 235, 246-7, 

 249, 250, 262, 265, 285, 

 293, 295-6, 301, 305, 309, 

 310, 315-8, 333, 378, 389, 

 411, 457, 482, 501, 569, 

 572, 640-1, 644 



integral, 482, 641 



parameter, 592-3 

 Epicycloid, 254 



Equation linear in 1 un- 

 known, 401, 690-1, 700 



quadratic in x and in y. 

 474, 625, 639-642 



with like first n coefficients, 

 714-6 



- polynomial coefficients, 

 695, 743 (see Pell) 



- x m + y> = z l with x, y, z 

 polynomials, 760, 774-5 



I** - v = 1, 731, 738, 

 744, 747, 752-5, 766 



ax m + by n = cz l , 698, 737- 

 8, 749, 754-5, 757-9, 761-2, 

 764, 766, 769, 771-6 



xv = y x , 687 



l/xi + . . . + l/x n = 

 I/a, 688-691 



Equivalent, 91, 96, 677 



Euclid's g.c.d. process, 45-49, 

 52, 53, 61, 93, 95, 352 



Every number a sum of cer- 

 tain numbers, 14, 22-5, 30, 

 144, 160, 429, 717, 719 (see 

 binomial, congruent, figur- 

 ate, geometrical, polygonal, 

 pyramidal, sum of squares, 

 triangular, Waring) 



four positive 



rational cubes, 727-9 



nine cubes, 



23, 717-725 



three rational 



cubes, 726-7 



represented by a 2 + 



2/3 2 + 3 7 2 + 6<5 2 , 263, 270 



Sz 4 + t/ 4 - z 4 - 



3u\ 728 



odd number represented 

 by 2x 2 + y 2 + 2 2 , 260, 264 



Exceptional prime, 741 



Factorial, 9, 124, 126, 143, 

 232, 679-682, 722 



Factoring, 395-7, 763 



Factors of (x + y) n x n 

 ?/", 737-8, 745-8, 751-5, 

 760-1 



Farey numbers, 149 



Fermat's theorem, 55, 171, 

 238, 251, 281 



Fermat's last theorem x n + 

 y n =(= z n , 731-775 (see alge- 

 braic, Bernouillian, class, 

 congruence, equation, fac- 

 tors, polynomial, regular) 



, n = 3, 545-550, 767 



, n = 4, 615-620, 



757, 761 



-, n = 5, 732-3, 735, 



738, 755, 760-1, 771, 773 

 -,n = 6, 732, 758, 772- 



3,776 



-, n = 7, 663, 737, 



739, 746-8, 761 



-, n = 10, 772 



, n = 11, 774 



, n = 14, 736 



, n = 37, 745, 755-6, 

 769 



, n = 59, n = 67, 

 745 



, n even, 736-7, 754- 



5, 765, 772-3 



, n fractional, 738, 

 756, 774 



, x, y, z polynomials, 

 749, 750, 757, 760, 770-1, 

 774, 775 



, criterion of Kum- 



mer, 744, 761, 765, 767, 775 



Mirimanoff, 



761, 768-9, 771 

 Wieferich, 764, 



766-8, 771, 775-6 

 Feuerbach's circles, 201 

 Figurate number, 5, 7-9, 13, 



14, 17, 18, 22, 23, 29, 33-5, 



39 

 , every number a sum 



of, 13 



generalized, 9 



Finite number of solutions, 



674-5, 764 

 Fourth power (see biquad- 



rate) 



Gamma function, 95, 97, 721, 

 725 



Generating function, 76, 137, 

 139, 148, 152-3, 157, 160 

 (101-164, implicitly) 



Genus of curve, 169, 592-3, 

 675-7, 775 



Geometrical methods, 55-6, 

 64, 66, 68, 73, 87, 95, 98, 

 166, 174-5, 219, 255, 274, 

 297, 318, 341, 388, 396, 425, 

 434, 471, 513, 542-3, 546-7, 

 555-7, 576 590-3, 596, 642, 

 644, 675-6, 687 (see genus, 

 lattice, tangent) 



progression, 105, 441, 

 443, 451, 453, 456, 602-3 



, every number a sum 



of terms of a, 105, 110, 112, 



164 



Girard's theorem, 228 

 Gitter (see lattice) 

 Gnomon, 1 

 Gonal (see polygonal) 

 Greatest common divisor, 



50, 51, 73, 74, 313, 772 (see 



Euclid) 

 Group, 696, 774 



Harmonical progression, 435- 



7 



Heptagonal, 2, 6, 10, 28 

 Hermitian form, 289 

 Heron angle, 199 



parallelogram, 207 

 , problem of, 485-7 



triangle, 191 

 Hexagon, central, 545 

 Hexagonal, 2, 6, 8, 18, 19, 



20, 25, 31, 38, 39 

 Hexahedral, 16 

 Hyperbolic function, 389 

 HypereUiptic curve, 677 



Icosahedral, 16, 23 

 Ideals (see algebraic) 

 Indices, 305-6, 357, 394 

 Infinite products, 13, 28, 31, 

 101-5, 113-6, 137, 140-1, 

 146, 148-9, 163, 234, 245, 

 313 317 



series, 13, 16, 19, 20, 24, 

 26, 31, 33, 71, 98, 101-6, 



