This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1919 Excerpt: ...di Mat., 25, 1887, 161-173. 1"Casopis, Prag, 18, 1889, 97; cf. Fortschritte Math., 1889, 30. F. J. Studnicka191 treated at length the solution in integers x, y (yV) of 6x+l=?/2, discussed by Leibniz in 1716. L. Gegenbauer192 gave a new derivation of the equations of Berger188 leading to asymptotic expressions for the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1919 Excerpt: ...di Mat., 25, 1887, 161-173. 1"Casopis, Prag, 18, 1889, 97; cf. Fortschritte Math., 1889, 30. F. J. Studnicka191 treated at length the solution in integers x, y (yV) of 6x+l=?/2, discussed by Leibniz in 1716. L. Gegenbauer192 gave a new derivation of the equations of Berger188 leading to asymptotic expressions for the number of solutions of x2=D. A. Tonelli193 gave a method of solving x2=c (mod p), when p is a prime 4/i+l and some quadratic non-residue g of p is known. Set p = 2'y + l, where y is odd. By Euler's criterion, the power y2" l of c and g are congruent to +1, --1. Set eo = 0 or 1, according as the power y2'2 of c is congruent to +1 or--1. Then 2-12-2= +i(mod p). For s3, set ii = 0 or 1 according as the square root of the left member is = +lor-1. Then G. B. Mathews77 (p. 53) treated the cases in which x2=a (mod p) is solvable by formulas. Cf. Legendre.166 S. Dickstein194 noted that H. Wronski169 gave the solution-d +MJ of zn--ay"=0 (mod M) with (1/1)2 in place of K, and gave, as the condition for solvability, o(1/1)'-1-0mod.M). But there may be solutions when the last condition is satisfied by no integer k. This is due to the fact that the value assigned to y imposes a limitation, which may be avoided by using the same expressions for y, z in a parameter K, subject to the condition aKn--1=0 (mod M). M. F. J. Mann194" proved that, if n=2V-., where X, M, ... are distinct odd primes, the number of solutions of xp=l(mod n) is GGiG2... 0i02 where G= 1 if n or p is odd, otherwise G is the g. c. d. of 2p and 2-1, and where Gi, G2, .., gi, g2l.. are the g. c. d.'s of p with X0-1, M-1)-., X--1, M--1, ..., respectively. A. Tonelli196 gave an explicit formula for the roots of x2==c (mod px), 0, 1,2, ... until we reach a number of the form z...
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Add this copy of History of the Theory of Numbers to cart. $12.63, good condition, Sold by ThriftBooks-Dallas rated 4.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1971 by Chelsea Publishing Company.
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Fine. Trade paperback (US). Glued binding. 504 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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New. Trade paperback (US). Glued binding. 504 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of History of the Theory of Numbers, Volume 1: to cart. $32.42, very good condition, Sold by BookDepart rated 4.0 out of 5 stars, ships from Shepherdstown, WV, UNITED STATES, published 1952 by Chelsea Publishing Company.
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Very Good. Hardcover, Volume 1 only; light fading, light shelf wear to exterior; other wise contents in very good condition with clean text, firm binding.
Add this copy of History of the Theory of Numbers to cart. $33.14, good condition, Sold by Bargain Treasures rated 5.0 out of 5 stars, ships from Iona, ID, UNITED STATES, published 1971 by Chelsea Pub Co.
