Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition, Chicago, 1893 (Classic Reprint)
Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition, Chicago, 1893 (Classic Reprint)
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ... " J 0 1 + e"'17 ce qui est la formule a laquelle nous voulions parvenir. ON THE DEFINITIONS OF THE TRIGONO-METRIC FUNCTIONS. THE PRINCIPLES OF THE ELLIPTIC AND HYPERBOLIC ANALYSIS. BY ALEXANDER MACFARLANE Op AUSTIN. These two papers have since been published as separate pamphlets by the author. No ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ... " J 0 1 + e"'17 ce qui est la formule a laquelle nous voulions parvenir. ON THE DEFINITIONS OF THE TRIGONO-METRIC FUNCTIONS. THE PRINCIPLES OF THE ELLIPTIC AND HYPERBOLIC ANALYSIS. BY ALEXANDER MACFARLANE Op AUSTIN. These two papers have since been published as separate pamphlets by the author. No abstracts have been furnished for publication here. Editors. ON FIFTH-POWER NUMBERS WHOSE SUM IS A FIFTH POWER. BY ARTEMAS MARTIN Of WASHINGTON. It is known that the sum of two fifth-power numbers cannot be a rational fifth power, but, so far as the present writer knows, it has not been proved that the sum of three, of four, and of five fifth-power numbers cannot be a fifth power. The writer, however, has not been able to discover fewer than six fifth-power numbers whose sum is a fifth power, and thus far has succeeded in finding only two such sets, although probably many exist. In the present state of algebraic science, fifth-power numbers whose sum is a fifth power can be most easily found by resorting to some artifice or some tentative process, two of which methods it is the object of this paper to present. 1. Take any two numbers p and q and put p"--qi = d; then, by transposition q + d=p (A). Now if d can in any way be separated into fifth-power numbers, all different and p not among them, we shall obviously have 5 +(these fifth-power numbers) = ps (B). Examples. 1. In (A), take p= 12, q = 11; then we have d = 87781 = 95 + 75 + 65 + 58 + 4; therefore by (B), 45 + 55 + 6" + 75 + 95 + ll5 = 125, six fifth-power numbers whose sum is a fifth power. 2. Take p = 30, q = 29; then d = 3788851 = 19s + 16 + ll3 + 106 + 5s; therefore 5" + 10s + IP + 1G5 +195 + 295 = 305, another set of six fifth-power numbers whose...
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All Editions of Mathematical Papers Read at the International Mathematical Congress Held in Connection with the World's Columbian Exposition, Chicago, 1893 (Classic Reprint)
