I am very happy that the moderator has permitted me to join this
group of mathematicians. I would like to put a new topic but
fundamental and may help in solving the great unsolved problems.
Kindly read this and comments are welcome. I have also solved
Goldbach Conjecture, I will complete it and send for publication.
Thank you all members.
Theory of Lower Index or Lindex
Amit D Kulkarni PSU Oregon
Prof. D M Kulkarni Pune, INDIA
Lower index or lindex of a number is defined as am = a ¡Â a ¡Âa ¡Â a ¡ m
times = a2 - m written as am, and is read as ¡®a lowered to m¡¯ with
self-division operation. Laws of lindices are similar to the laws of
indices. Every natural number is associated with index and lindex.
Combination of lindex and index of a number anm where m is an index
and n is lindex is defined and is equal to
am ( 2 ¨C n ) . Similar to logarithms, golarithms golaN =m can be
defined on the basis of lindices and its relation to logarithms can
be established. The relation between imaginary numbers and lindex 1/2
of -1 called as div root is ¦«-1 = (-1)1/2 = -i and (-1)3/2 = i is
defined. The above results are based on the definition and concepts
in elementary mathematics and no attempt has been made to explain the
theory and the applications of lindices.