prove that zero is divisible by every integerSolutionis not

prove that zero is divisible by every integer

Solution

is not divisible by every integer, since 0 is not divisible by 0 (and 0 is an integer)
0/0 gives an indeterminate result

However, 0 is divisible by every positive or negative integer.

Let x be a non-zero number:

0/x = y
0 = y * x

Since y * x = 0, then one of y or x = 0
Since x is non-zero number ---> y = 0

0/x = 0 for all non-zero numbers x (i.e. 0/x leaves no remainder)
? 0 is divisible by x, where x is any non-zero number