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Notes on Explorations 403 f(k-i) E f(k+i) (mod q) f or each integer i, it can be argued that u 5 k. We have 4k(k-1)+1=q2< f(u ...
404 Notes on Explorations then y belongs to S if and only if y is a positive value assumed by the polynomial g(y,x). A survey ar ...
Notes on Explorations 405 the coefficient of x’ in the expansion of (1 + x)“, from Horner’s table we find that ... It can be sho ...
406 Notes on Explorations In dealing with polynomial divisors with more than one distinct zero, the divided difference technique ...
Notes on Explorations 407 of Functions: Parts I and II; Problem Book in the Theory of Functions: Volumes I and II. E.26. There a ...
408 Notes on Explorations (i.e. i!” - fk(a)t + a&l(a) is a multiple of t2 - t + a) where fl(a) = 1, fi(a) = 1 and fk+l(U) = ...
Notes on Explorations^409 E.30. The sequences ~~(4) and ~~(6) arise in the following context. The number 5040 is not only 1 less ...
410 Notes on Explorations The reader may wish to explore further the intervention in the factorization of the Fibonacci sequence ...
Notes on Explorations^411 Intelligencer 9 (1987), no. 2, 53-60. Also see P. Erdos & R.C. Vaughan, Bounds for the rth coeffic ...
412 Notes on Explorations. of a polynomial, Amer. Math. Monthly 27 (1920), 299-300 it is shown that, for a polynomial f(z) with ...
Notes on Explorations 413 For a general introduction on the nature of the real number field, which includes a chapter on continu ...
414 Notes on Explorations sums. The paper C. Kelly, An algorithm for sums of integer powers, Math. Mug. 57 (1984)) 296-297 gives ...
Notes on Explorations 415 , (i) m = 2, n is even; (ii) n = 2, m is arbitrary; (iii) m = 3, n = 4. See Section 2.23 of the above ...
Glossary abscissa the first coordinate of a point in the Cartesian plane arithmetic progression a sequence in which the differen ...
Glossary odd function a function f satisfying f (-x) = -f(x) 417 one-one correspondence function from one set onto another which ...
418 Glossary Q the field of rational numbers R the field of real numbers C the field of complex numbers Heron’s Formula The area ...
Further Reading A gentle first reader is the Mir tract by Kurosh. Designed for a one- semester course is the book by MacDuffee ( ...
420 Further Reading See also DH, Ch. 3, for a general discussion of solvability. An historical survey of the theory of equations ...
Books A.D. Aleksandrov, A.N. Kolmogorov & M.A. Lavrent’ev (eds.), Mathemat- ics: Its Content, Method and Meaning (3 volumes) ...
422 Books Richard J. Crouse & Clifford W. Sloyer, Mathematical Questions From the Classroom Prindle, Weber & Schmidt, 19 ...
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