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|Diophantine Equation above procedure can be simplified by noting that the two |
left-most columns are offset by one entry ... EQUATION-2ND POWERs,
DIOPHANTINE EQUATION–3RD POWERS, DIOPHANTINE EQUATION-4TH
|... green, yellow, purple, the square of green, and yellow balls, then sum of both is |
equal to the 3rd power of purple balls ... Find the values of x, y, z of the
Diophantine equation x2 + y2 = 20z2 (x, y, z are the whole numbers) *) Find the
values of ...
|Diophantine equation Mathematics, an algebraic equation with integer |
coefficients and two or more variables, ... DiophantUS 3rd century ad Greek
mathematician; called the father of algebra for his use of ... a unit of measure of
the refractive power of a lens, equivalent to the power of a lens with a focal length
of one meter; ...
| Danicic, I. The solubility of certain Diophantine inequalities. Proc. London |
Math. Soc. ...  Davenport, H. On Waring's problem for fifth and sixth powers.
American J. Math., 64, ... Springer- Verlag, 3rd edition, 2000.  Davenport, H.
|A Diophantine equation (named in honour of the 3rd-century Greek |
mathematician Diophantus of Alexandria) is an ... the variables to be integers
only, i.e. an equation involving only sums, products, and powers in which all the
constants are ...
|Diophantine equations involve only sums, products, and powers in which all the |
constants are integers and the only solutions of ... Named in honour of the 3rd-
century Greek mathematician Diophantus of Alexandria, these equations were
|... applications of algebra to regular polygons; and practical problems, including |
Diophantine equations, a 3rd-century Greek analytical method ... Abu Kamil went
beyond the simple x2 to arrive at higher powers of numbers, up to the power X8.
|J. 8, 149–159 (1961) Guy, R.K.: Unsolved Problems in Number Theory. Springer, |
Berlin (1981); 2nd ed. 1994, 3rd ed. 2004 Gyires ... (Debr.) 52, 1–31 (1998) Gy
̋ory, K.: Power values of products of consecutive integers and ... 237–265. de
Gruyter, Berlin (1999) Gy ̋ory, K.: Solving Diophantine equations by Baker's
|As a background to (1.1) it is illuminating to look at how the special equations (|
2.1) are solved by current methods of algebraic number ... We have y + i = d(a +
bi)3 with a, b € Z. But d is anyway a 3rd power in Z[i] and so may be ignored here.