Prove the following statement about divisibility of integers:
If d|(a+b) and d|a, then d|b.
Solution
we can write d =(a+b) where is an integer;
also d= \'a where \' is an integer
\'a = (a+b) => (\'-)a = b => {(\'-)/}a = b.........(1)
If d is divisible by b then d=\"b => d=\" {(\'-)/}a [\" is an integer] [Putting value of b from (1)]
\" {(\'-)/} is also an integer and thus d is divisible by a as given in the ques.......
Thus our assumption is correct
Thus d is divisible by b........
Hope you understand the explanation.
Prove the following statement about divisibility of integers If d.pdf
1. Prove the following statement about divisibility of integers:
If d|(a+b) and d|a, then d|b.
Solution
we can write d =(a+b) where is an integer;
also d= 'a where ' is an integer
'a = (a+b) => ('-)a = b => {('-)/}a = b.........(1)
If d is divisible by b then d="b => d=" {('-)/}a [" is an integer] [Putting value of b from (1)]
" {('-)/} is also an integer and thus d is divisible by a as given in the ques.......
Thus our assumption is correct
Thus d is divisible by b........
Hope you understand the explanation
![Prove the following statement about divisibility of integers:
If d|(a+b) and d|a, then d|b.
Solution
we can write d =(a+b) where is an integer;
also d= 'a where ' is an integer
'a = (a+b) => ('-)a = b => {('-)/}a = b.........(1)
If d is divisible by b then d="b => d=" {('-)/}a [" is an integer] [Putting value of b from (1)]
" {('-)/} is also an integer and thus d is divisible by a as given in the ques.......
Thus our assumption is correct
Thus d is divisible by b........
Hope you understand the explanation](https://image.slidesharecdn.com/provethefollowingstatementaboutdivisibilityofintegersifd-230326113950-4117bc2c/85/Prove-the-following-statement-about-divisibility-of-integers-If-d-pdf-1-320.jpg)
