Prove that 11, 12 and 13 can never be three terms (not necessarily consecutive) of a geometric progression
, irrespective of whether the common ratio is real or complex.
not sure if this
r^z=13 for some integers x,y,z
from r^z=13 we have z*ln(r)=ln(13) thus
but the left hand side is simple the log of 12/11 to the base 13, this is an irrational number thus can not be equal to (y-x)/z for integers x,y,z. Thus 11,12,13 can not be part of the same geometric series.
Posted by Daniel
on 2009-09-19 21:47:49