Question

Understanding this proof for the proposition "For all integers a, gcd(9a+4, 2a+1) = 1.

Proof: gcd(9a+4, 2a+1) = gcd(2a+1, a) = gcd(a, 1). Since gcd(a, 1)=1, gcd(9a+4, 2a+1) =1.

I don't understand what they are doing in this proof? How did they find all this?

Answer 1

first line because 4(2a+1)=8a+4 and 9a+4-(8a+4)= a

Answer 2

second line because a times 2 =2a and 2a+1-2a=1

Answer 3

although the second equality is more or less obvious since 2a+1 leaves a remainder of 1 when divided by a

Answer 4

good morning myininaya
how was early am calc?

Answer 5

i'm kindof mad my class stood me up
i could have slept longer
one student showed i thought integration by parts lol

Answer 6

taught*

Answer 7

oh i like that line
one student shows up, and you will definitely be having integration by parts
part today,
part next class,
part next week...

Answer 8

i was like heres 5 bonus points enjoy

Answer 9

i think i will give a quiz on integration by parts tomorrow

Answer 10

sounds good
now if i don't get out of here and finish my work, i am going to be in real trouble

Answer 11

good idea!

Answer 12

lol all of them will fail except that one

Answer 13

right! it must be annoying. i had a class where about half showed up last week, so we did fun stuff

Answer 14

i taught them how to add

Answer 15

lol
integration by parts is fun

Answer 16

actually i think so too

Answer 17

i showed the one student the table
i will not show the table anymore
hes the only one who gets the easy way

Answer 18

maybe he will share the secret
off to the garage, see you later

Answer 19

don't leave me
i forgot -1 comes before 0
i need your help

Answer 20

what problem?

Answer 21

minus one comes before zero?

Answer 22

its the problem before this one
i feel like an idiot
i was like choose a number before -1 like 0

Answer 23

there is a limit problem for you to do, x - sinx etc
i will look at your problem