Class Notes
(806,815)

Canada
(492,451)

University of Waterloo
(18,164)

Mathematics
(1,874)

MATH 135
(334)

Jennifer Nissen
(1)

Lecture 14

# Linear Diophantic Equation Lecture 14

Unlock Document

University of Waterloo

Mathematics

MATH 135

Jennifer Nissen

Fall

Description

ecture 14 Lin
Diophantine Equall
ons (LDE s)
Ex 12.2
S3
53
for we saw
(-35) -13
Gurs in Does 1053 Y ugty 39 hava, a solution r y 2
yes
53 C4
49 09) 3
53
But 3 t co se there cannot be an integer southen.
uations of the form ax by C a b an el where are
cearching for integer men s are el Linear Deehantine Eg rottens
is a line
How do wn. find ano integer sc tutuon
mother
LOS 7'yecrem 3.
(i) me tocar di Phan tune Equator. o by c has a courtron rff the
(in) gc-1 tab) d c an d x s ro and y yo ic a part cerar
cotu ticn then the compre e integer sofution i s X Xe n
A particular sofu it on scruticn tu "re prvolem you can d core by
EA k reser t EEA or inspl ction.
Thu comptete se .c solutient equation
Does et har have a se uticrt
ged (702 2 G Loheck)
so has no solutten out 2nd has infrnitely m ony to (utrcus
so tution X G8
Complu Sol een is
S3 ICs
ecture 14 Lin Diophantine Equall ons (LDE s) Ex 12.2 S3 53 for we saw (-35) -13 Gurs in Does 1053 Y ugty 39 hava, a solution r y 2 yes 53 C4 49 09) 3 53 But 3 t co se there cannot be an integer southen. uations of the form ax by C a b an el where are cearching for integer men s are el Linear Deehantine Eg rottens is a line How do wn. find ano integer sc tutuon mother LOS 7'yecrem 3. (i) me tocar di Phan tune Equator. o by c has a courtron rff the (in) gc-1 tab) d c an d x s ro and y yo ic a part cerar cotu ticn then the compre e integer sofution i s X Xe n A particular sofu it on scruticn tu "re prvolem you can d core by EA k reser t EEA or inspl ction. Thu comptete se .c solutient equation Does et har have a se uticrt ged (702 2 G Loheck) so has no solutten out 2nd has infrnitely m ony to (utrcus so tution X G8 Complu Sol een is S3 ICsRhet Theorem 2.30
i) Assume ay by c has a scrutten
ie. 2 Such that
ax t by C
gcd ka, b) a and d
(a b) b
9cct
P'UP
Let d ged ca, b) Assume.
Sincs eltc 39 c a such nat c zd
By EEA
3 a so tutuin to ax by d
Let x xe, y yo be tha
particuror ser tre

More
Less
Related notes for MATH 135