Answer:
Part a) (a,b,c)=(10,19,9)
Part b) (a,b,c)=(9,3,1)
Please let be know if I have interpreted your question correctly. Thank you.
Step-by-step explanation:
Part a)
This is the way I interpret part a:
Find integers a,b,c such that a|(b-c) but a does not divide b and a does not divide c.
There are many triples satisfying part a.
One such triple is (a,b,c)=(3,10,7).
3 divides 10-7
But 3 does not divide 10 and 3 does not divide 7.
Another example is (a,b,c)=(2,7,5).
2 divides 7-5
But 2 doesn't divide 7 and 2 doesn't divide 5.
I will give another example.
(a,b,c)=(10,19,9)
10 divides 19-9
But 10 doesn't divide 19 and 10 doesn't divide 9
Part b)
This is the say I interpret part b:
a | (2b + 3c) but a does not divide b and a does not divide c
So lets let b=2 and c=5, then 2b+3c=19.
We just need to choose an a such that it divides 19 but not 2 and 5. That should be easy. 19 itself will do that.
So one (a,b,c) could be (19,2,5).
Let's try for another example.
Let b=3 and c=1.
Then 2b+3c=9.
So we just need to find an a that divides 9 but not 3 and not 1.
9 works.
So another example is (9, 3,1).
