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|746 Diophantine Equation 873 + 2333 + 2643 + 3963 -t- 4963 + 5403 = 903 -I- |
206 ' + 3093 + 3663 + 5223 + 5233 . ... D. Personal communication, Apr. 17, 1997
. r 1999-001 Wolfram Research, Inc. Diophantine Equation 4th Powers As a ...
|Volume I: Tools and Diophantine Equations Henri Cohen ... ADF A AF AE ADF |
Sums of Two Rational Fourth Powers up to 10000 An amusing corollary of this
table is the following result, due to Bremner and Morton [Bre-Mor]: Corollary 6.6.
|The diophantine equation x4 y4 = z2 has no nontrivial solutions, as can be |
shown using the method of infinite ... Euler conjectured that there were four fourth
powers of positive integers whose sum is also the fourth power of an integer.
|S. Brudno, On generating infinitely many solutions of the diophantine equation |
A6 + B6 + C6 = D6 + E6 + F6, Math. Comput. ... htm J. Choubey, Parametric
solutions of Diophantine equation with equal sums of four fourth powers, Acta
|Hence we may suppose that equation (20) is in the normal form, i.e. (X, Z) = (Y, Z) |
= (X, Y) = 1, (A, B) = l, (A, d) = (B, ... On the diophantine equationF = ax4 + by +
cz4 + dw' = O, the product abcd being a square number. ... three fourth powers.
|In American Mathematical Monthly 75 (1968), 1061-1073, L.J. Lander studies |
equal sums of like powers, in particular, sums of two fourth powers and of three
and four fifth powers. 30. See the expository articles by Cox and by ... Additional
Reading R. D. Carmichael, On the impossiblity of certain diophantine equations
and systems of equations. American Mathematical Monthly 20 (1913), 213-221.
|looks like the beginning of a most interesting sequence of equations! But alas, as |
the reader will easily verify, the expected third equation involving the sum of four
consecutive fourth powers does not hold, and indeed no sum of four consecutive
fourth powers is a ... Let us now consider the Diophantine equation x2 + y2 = z2.
| Davenport, H. On Waring's problem for cubes. Ada Math., 471, 1939:123-143|
.  Davenport, H. On Waring's problem for fourth powers. Annals of Math., 40,
1939:731-747.  Davenport, H. On Waring's problem for fifth and sixth powers.
|Equations that work only on whole numbers are called Diophantine equations (|
after the Greek mathematician Diophantus). ... Diophantine equations): It is
impossible to separate a cube into two cubes, or a fourth power into two fourth
|Prove that no integers x and y exist such that the difference of their sixth powers |
is a square. 3. Prove that no relatively prime integers x and y exist such that the
difference of their fourth powers is a cube. 4. Show that the equation x--\-y3=z* is
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