Question

Please explain this property of divisibility . It 's urgent.​

Answer 1

Here , it is written that -

' If a and b are non zero integers, then

a | b and b | a => a = $\sf{ \pm}$ b . '

Explaination -

Here , we have assumed that a and b are both non zero integers and dont have any definite order .

Now , we have the information given -

a | b and b | a

Now ,

If ,

a | b

, a has to be less than or equal to b and b needs to have a as a factor .

If

b | a

, b has to be less than or equal to a and a needs to have b as a factor .

So , there arises two inequalities -

$\sf{ a \leqslant b }$

$\sf{ a \geqslant b }$

For a and b both non zero , equality holds if and only if a = $\sf{ \pm}$ b . '

Hence, this statement is true .

Additional Information -

If a | b and a | c , then a | bc.

If a | bc but a does not divide b , a is a factor of c.

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