00:01
Hi, in this question, given that a and b are relatively prime and also given that d divides both ac and bc, we have to prove d divides c.
00:38
Since d divides ac and bc, so we can write it as ac equals dm and bc equals dn, where m and n are integers.
00:55
Next, we have to consider the product ab.
00:59
So, ab can be written as a into dm, which is equal to adm.
01:06
Similarly, we can write it as ab equals b into dn, which is equal to vdn.
01:14
Since ab has two different expressions, it follows that ad equals bd, since both equal ab.
01:28
Now, a and b are relatively prime, so that the greatest common divisor of a and b is 1.
01:40
This means that a and b share no common prime factors...