Question

plse some one tell me
from following, which is not true.

Answer 1

what math class is this from?

Answer 2

Remember that a, b, x, y are integers. Let's go through them all one by one:

a) (a.b) = 1 (assuming this means a times b = 1, which means both integers a and b must be 1, so 1x + 1y = 1... this is true if either x or y is zero, and the other is 1.

b) (x,y) = 1... assuming this means x and y equal 1? 1a+1b=1, true just like the first.

c) (a,y) = 1... 1x+1b=1, true just like the first two.

d) (b,y) = 1... ax+1*1 = 1, true if a or x is zero.

I guess I don't get it then :/

Answer 3

@agent0smith
i have done same method, by putting the value, but not getting an answer

Answer 4

They're all true as long as a,x,b,y can be zero if necessary.

Tell your teacher "Your question is bad and you should feel bad!"

Answer 5

It seems like it needs more info, like that they're distinct integers, to make it an actual (ie not pointless) question.

Answer 6

hmm u r right

Answer 7

a) (a.b) = 1 (assuming this means a times b = 1, which means both integers a and b must be 1, so 1x + 1y = 1... this is true if either x or y is zero, and the other is 1.

a and b could also both be -1 here, and then a.b = 1... not that that changes anything:
-1x - 1y = 1... still true if x=-1 and y=0, or x=2 and y=-3 (etc etc, there's a bunch of solutions)

Answer 8

dont rational fractions count as integers?

Answer 9

http://www.techterms.com/definition/integer

http://www.thefreedictionary.com/integer

Answer 10

when you say
(a,b)
I believe that should imply a "GCD" of a and b

Answer 11

then D would be the answer!

Answer 12

how

Answer 13

That seems reasonable... it'd be nice if it was clearer. It looks like it should be "gcd(a,b). Some older textbooks use (a,b)"

Answer 14

@electrokid

d) (b,y) = 1 so let's say b=3 and y=2. They have a GCD of 1.

ax+3*2 = 1, if a=5 and x=-1, this is still true.

Answer 15

yes. this would then seem to go indefinetly unless some restrictions are imposed on the system

Answer 16

what restrictions

Answer 17

using Theorem 2 from this reference http://web.mit.edu/6.857/OldStuff/Fall02/handouts/L07-generators.pdf
it seems that gcd(x,y) may not always be = 1

Answer 18

but these type of theorems i, m reading first time

Answer 19

the question is obviously based on number theory but the symbols in the question are not quite clear.

Answer 20

leave it
but any way thank u friends @agent0smith & @electrokid