Divisibility

Theorem
Let a, b be integers. Then a is divisible by b if and only if there exists an integer k such that a = b*k.
 
Remark

a|b,

divisibility(a, b) = true or false.

 
Example

let a = 49, b = 7,

then 49 = 7*7, here k = 7.

 
Divisibility of zero:
Lemma
divisibility(0, b) = true.
 
Example

let a = 0, b = 7,

divisibility(0, 7) = true,

we known that, a = b*k ,

i.e., 0 = 7*0, here k = 0.
 

In-fact, b can be any integer.

From the above example we can conclude that,

every integer divides 0.

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