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.
4.18.24 Movement Legacies, Reflection, and Review.pptx
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-dpdf-1-320.jpg)
