Suppose . Also, . Let . Then . Then . Or . Or .
We know that . So . Also , which forces the quotient to be positive. If then . So so that the quotient is negative.
if a and b are integers and (a+b* sqrt(11) )> 1 and (a+b* sqrt(11) )* (a-b* sqrt(11) )=1, how do i show that a and b are positive integers? I was able to prove b>0 , but i can't seem to get the a >0 part, which makes me doubt whether i really showed b>0 .
Thanks