Sodium and water content of muscle responded in a more complex pattern ... sed free water clearance evident within two hours after intravenous inoculation with.
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We know that while the equation x2 + y2 = z2 has infinitely many solutions in integers, the ... For that we study this problem by showing the following results: .... To find the solution of the above diophantine equation, we will study four cases.
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unit, which under certain conditions is the fundamental unit, and are important in studying the Diophantine Equation x. + y3 + z. 3. KEY WORDS ... i, and q i, then solving x. +12Ax. 12 y2 is equivalent to solving -AG4 -2 G3H + 3 H4=-I. (This has ...
ON THE COMPUTATION OF THE CLASS NUMBERS OF SOME CUBIC FIELDS MANNY SCAROWSKY and ABRAHAM BOYARSKY Department of Mathematics Loyola Campus Concordia University Montreal, Canada H4B IR6
(Received December I0, 1985)
ABSTRACT.
x3+12Ax-12
Class numbers are calculated for cubic fields of the form
A > 0, for
!
and for some other values of
! 17
a
A.
0,
These fields have a known
unit, which under certain conditions is the fundamental unit, and are important in
studying the Diophantine Equation
+ y3 +
x
Class numbers, cubic fields, Diophantine equation.
KEY WORDS AND PHRASES.
12A04, 12A50.
1980 AMS SUBJECT CLASSIFICATION CODES.
I.
3.
z
INTRODUCTION AND SOME THEOREMS. We consider the cubic fields defined by an equation of the form
(I.I) 0, 12 to related is it because is important equation The field defined by this f(x)
A > 0.
where
the Diophantine equation
+ y3 +
x
when
3
z
9a 2 [i].
A
Equation (I.I) is
f(x) is increasing, it defines a real cubic field (with two complex conjugates) with exactly one fundamental unit. Let @ be the real and as
