Index 439parabola, 143 (4.5.1), 155 (4.9.2),
319
partial derivatives, 68-71,406-407
partialfractions, 108-110, 117-118,
281-283
Pell’s equation, 373 (8.11), 396-
397,409-410
permutations, 133-135
pirate problem, 15, 45, 248
polygon, 116 (3.8.29), 148, 262,
296
polynomials of several variables
composition, 238
definitions, 24-27
elementary symmetric func-
tions, 24, 25, 193, 251,
384
homogeneous, 24,25,27,59-
61,87, 117, 251
range, 28, 400
symmetric, 24, 27,43, 59-61,
112 (3.7.21), 251,260,383-
384
polynomials of single variable
anatomy of, 1
commuting, see composition
of polynomials
evaluation of, 2, 49-53
even and odd, 6 (1.1.19), 245,
416-417
operations on, 2, 4, 56-59
real coefficients, 16, 146-147
uniqueness of representation,
5
positive polynomials, 43 (1.9.11,
12), 47-48,220,224,259-
260,414
powers of numbers
evaluation, 53, 404
sums, see sums of first n pow-
ers
Tarry-Escott problem, 6,394-
396
powers of roots, sum of, 198-200,
347
primes, 31
decomposition, 33, 252
values of polynomials, 35,402-
403
primitive root of unity, 102, 117,
280
principal part, 411
Putnam Competition, xiv, 365,400quadratic residue, 103
quadratics, 2, 6, 9-12
common zero, 122-123
completion of square, 9, 72,
334 (5.4.15)
complex coefficients, 16, 140
continued fraction, 169
discriminant, 9,45,119 (3.8.7,
ll), 139, 147, 196, 248,
250, 253, 254, 257, 286,
290, 341, 344-345, 370,
372,409
factoring, 84-85
graph, 72, 265
graphical solution, 12, 396
hints, 45, 46-47
interpolation, 206
intersecting curves, 138-140,
301
location of zeros, 115, 181,
187
nature of zeros, 76, 115, 139,
267, 272, 295, 333
over quaternions, 240
over Z,, 39, 114, 120
problems, 9-12, 39-42
solutions, 246-247, 252-258
square values, 13, 396-398
sum and product of zeros, 9-
10, 25,371
sums of powers of zeros, 199
winding around origin, 143-
145,303-305
quartics, 2, 20-21, 57, 195-196,
307
biological species, 160