Question

prove or disprove: If a divides bc, then a divides b or a divides c

Answer 1

let b=3, c=4, a=6

Answer 2

-sigh


here is a variable-based counterexample.

(Clearly, a must be greater than 1 since otherwise it is true! 1 divides every integer.)

Let b = a+1 and c = a-1
Then, b+c = 2a

Obviously a divides b+c since a divides 2a.

But since a>1, a cannot divide b since b ≡ 1 (mod a)
and a cannot divide c since c ≡ -1 (mod a)

Answer 3

got it?

Answer 4

yeah, i think so. thanks.

Answer 5

to disprove a statement, all you need is one counter-example.