- #1
SamitC
- 36
- 0
Hi,
One silly thing is bothering me. As per one lemma, If a, b, and c are positive integers such that gcd(a, b) = 1 and a | bc, then a | c. This is intuitively obvious. i.e.
Since GCD is 1 'a' does not divide 'b'. Now, 'a' divides 'bc' so, 'a' divides 'c'. Proved.
What is bothering me is : suppose bc/a = s. Then as = bc. Thus a = (b/s) c ... (1)
Now, if c/a is an integer so is s/b. Which means b/s is not an integer. Putting this in (1) - how 'a' divides 'c'?
Thanks in advance
One silly thing is bothering me. As per one lemma, If a, b, and c are positive integers such that gcd(a, b) = 1 and a | bc, then a | c. This is intuitively obvious. i.e.
Since GCD is 1 'a' does not divide 'b'. Now, 'a' divides 'bc' so, 'a' divides 'c'. Proved.
What is bothering me is : suppose bc/a = s. Then as = bc. Thus a = (b/s) c ... (1)
Now, if c/a is an integer so is s/b. Which means b/s is not an integer. Putting this in (1) - how 'a' divides 'c'?
Thanks in advance