The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

This discussion is now closed.

Check out other Related discussions

factor proof (degree maths)

Prove a|(b+c) if a|b and a|c | means is a factor of
Since a|b there is an integer z such that b=az
Since a|c there is an integer w such that c=aw
Adding gives;
b+c = az + aw
---> =a(z+w)
Since z+w is an integer, this is true a|(b+c)

Based on this proof how do you work out these;

1. a,b,c,d and e are integers
suppose a|b and a|c
prove a|(db+ec)

2. suppose a, b and c are integers
suppose also that a|b and b|c
prove that a|c

3. suppose that a and b are integers
suppose also that a|b and b|a
prove that a=b or a=-b

any help will be much obliged
Reply 1
Avatar for JamesF
JamesF
1
manps
Prove a|(b+c) if a|b and a|c | means is a factor of
Since a|b there is an integer z such that b=az
Since a|c there is an integer w such that c=aw
Adding gives;
b+c = az + aw
---> =a(z+w)
Since z+w is an integer, this is true a|(b+c)

Based on this proof how do you work out these;

1. a,b,c,d and e are integers
suppose a|b and a|c
prove a|(db+ec)

2. suppose a, b and c are integers
suppose also that a|b and b|c
prove that a|c

3. suppose that a and b are integers
suppose also that a|b and b|a
prove that a=b or a=-b

any help will be much obliged

Whenever you know that x|y for some x and y, you can write y = nx for some n, and then the answers all fall out.
Reply 2
Avatar for SsEe
SsEe
13
1. If a|b and a|c then there exist integers k,j such that b=ak and c=aj
So db+ec = dak+eaj = a(dk+ej) and a|[a(dk+ej)]

2. b=ak and c=bj=a(kj). So a|c

3. b=ak and a=bj
So b=bjk. jk=1.
So either j=1 and k=1 => b=a and a=b
or
j=-1 and k=-1 => b=-a and a=-b
Reply 3
Avatar for manps
manps
OP
im not with you

say for number 2,
if a|b and b|c, first of all could you say c|b, if so then
a|b.......b=az
c|b.......b=cw
az=cw

but this still gets me no closer to proving that a|c and for Q1 i cant get the end result :frown:
Reply 4
Avatar for JamesF
JamesF
1
manps
im not with you

say for number 2,
if a|b and b|c, first of all could you say c|b, if so then
a|b.......b=az
c|b.......b=cw
az=cw

but this still gets me no closer to proving that a|c and for Q1 i cant get the end result :frown:

No, b|c does not imply c|b unless b = +- c
Reply 5
Avatar for JamesF
JamesF
1
What university are you at btw?
Reply 6
Avatar for manps
manps
OP
SsEe
1. If a|b and a|c then there exist integers k,j such that b=ak and c=aj
So db+ec = dak+eaj = a(ak+ej) and a|[a(ak+ej)]


why is it
So db+ec = dak+eaj = a(ak+ej)...

and not

So db+ec = dak+eaj = a(dk+ej)
Reply 7
Avatar for JamesF
JamesF
1
manps
why is it
So db+ec = dak+eaj = a(ak+ej)...

and not

So db+ec = dak+eaj = a(dk+ej)

typo
Reply 8
Avatar for manps
manps
OP
ok i think im clear now,
cheers james and other guy

Related discussions

Latest

Trending

Trending

Articles for you