Thursday, 30 June 2016

elementary number theory - Prove if nmidab, then nmid[gcd(a,n)timesgcd(b,n)]

Prove if nab, then n[gcd(a,n)×gcd(b,n)]



So I started by letting d=gcd(a,n) and e=gcd(b,n).
Then we have x,y,w,z so that dx=a, ey=b,dw=ez=n
and we also have s so that ns=ab




or ns=dexy.



what I want is nde, but I'm only getting to nde(xy) since I cannot prove that s/(xy) is an integer.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...