show 5 divides ab, then 5 divides a or 5 divides b. not divided by.?

Question

show true with proof or counterexample.

Answer 1

Here's the easy approach.
First, suppose that 5 doesn't divide a and 5 doesn't divide b.
Then prove that under these conditions, 5 doesn't divide ab.
This shows that if 5 divides ab, then it can't be true that 5 doesn't divide a or b.
With that, your proof is done. :-)

Answer 2

5 is prime => 5=5*1 5|a=>a=5*z+0 using euclid's algorithm let B be any R# then a*B=(5*Z+0)*b+0=5*Z*B+0 since r= 0 5 divides a*B let 5|B and rewrite proof. since this is a dichotomous situation a and B cannot be indiviisble by 5 and simultaneously have the product be divisible by 5