. Suppose that c and d are given integers with d > 0. There are integers x and y such that (x,y) = d and xy = c if and only if d2 c. Let d = (a, b). Then a I be if and only if -Qd- is a divisor of c....

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. Suppose that c and d are given integers with d > 0. There are integers x and y such that (x,y) = d and xy = c if and only if d2 c. Let d = (a, b). Then a I be if and only if -Qd- is a divisor of c.
Problem 3. Consider a function f : D --* 111, and suppose that for every a E D there exist Ea > 0 and a neighborhood Na of a such that f(x) > Ea for all x E Na, n D. . Prove that if D is a compact, then,there exists E > 0 such that f (x) > E for all x E D. Give an example to show that :the conclusion of the previous statement need not hold if the assumption that D is compact is omitted.


Answered Same DayDec 20, 2021

Answer To: . Suppose that c and d are given integers with d > 0. There are integers x and y such that (x,y) = d...

Robert answered on Dec 20 2021
128 Votes
The answer is FALSE, that is for
,
cd
Î
¢
there do not exist integers
,
xy
such that
(

)
,
xyd
=
and
xyc
=
if and only if
2
|
dc
Suppose it is true that for
,
cd
Î
¢
there exist integers
,
xy
such that
(
)
,
xyd
=
and
xyc
=
if and only if...
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