Question

question: if a|c and b|c and gcd(a,b)=1, then ab|c
any hints? and how do i know that a*b 13 years ago

Answer 1

are these triangles? or is there anymore to the problem?

Answer 2

If a|c, the c = k*a, where k is an integer.

Answer 3

@dave0616 no i think its something related to modular arithmetics and greatest common divisor

Answer 4

If a|c, the c = k*a, where k is an integer.
If b|c, the c = j*b, where j is an integer.

Answer 5

listen to @tkhunny they know what their talking about haha

Answer 6

a|c => there exists an integer m s.t c=ma => a=c/m
b|c => there exists an integer n s.t c=nb => b=c/n
gcd(a,b)=1 => by Euclid's algorithm, there exist integers x, y s.t ax+by=1.
=> (c/m)x+(c/n)y=1 => (xn+ym)c=mn => (xn+ym)cab=mnab=(ma)(nb)=c^2 => (xn+ym)ab=c, which means ab|c (since xn+ym is an integer) (Q.E.D)

Answer 7

@drawar thank you so much....