Post by Peter FairbrotherThat cam out wrong, should be e^(2^n) mod p maybe?
e to the power (2 ^n) mod p
I don't know how to do multi-level superscripts in newsgroups, sorry.
Peter F
Post by Peter FairbrotherIs the set e^2^n mod p (where e is a generator and element of the
multiplicative group mod p, p is prime and n=0 to p) equal to the set
of quadratic residues of the group?
Thanks
Peter Fairbrother
How about "where it is and where it isn't".
Conjectures, in the infinitary, are, abstract.
Here you can find a bit of square-free,
for example to make a conjecture,
then for example running out conjectures,
yet it's so that: in the infinitary,
like "when there are infinitely many residues"
and "there are infinitely many powers of e to
the 2n", how "e is usually log-normal", with
regards to "whatever's log normal to e,
when the exponent is also an exponent here 2^n",
that the inverse of exponent or log, is also
for making the inverse of 2^n, out of exponent,
in 2's-log and e's-log, those being inverses of
a sort, that it's b to the a to the n, those
"inverses" having "what it log" and "what is out
square log".
Then, conjectures in the infinitary are also
abstract, this is basically "whether or not
there is a point at infinity" and "whether or
not the point at infinity is a prime" and
"whether or not the point at infinity is
a double prime", and for example "... or a composite",
and "... of so many or all factors", a double trime,
a triple prime, a quadruple prime, each an abstract
model of numbers, making its own independent
infinitary conjectures.
Then also things like the quadratic sieve or
here the "Factorial/Exponential Identity",
is out in large spaces of numbers, about
emergence of convergence criteria, with
the fact that number theory is independent
a lot of things for "point at infinity" for
whatever the "point at infinity" is, in laws
of large numbers.
The quadratic starts adding up from the parabolic
and the quadratic sieve, that's in primes of the
squares, the quadratic sieve, then the parabola
also _focusing_ what falls into it, for example
is in the effects of focusing what goes out
"exponentially" in phase state transition, with
regards to phase being potentials in power,
"on and off" for example when "if it changed
must have gone exponential", then with regards
to being linear or exponential in a, b, c,
is just pointing out that for the expression,
are "laws of large numbers" and "criteria of convergence",
that the laws are theoretically "underdefined", "it is the law",
while criteria or unknowns yet emergent, "it is its law",
that "expressions in the infinitary always assume a
law of large numbers", then that they don't in the linear,
or algebra results balanced or reduced quotients,
the product inverses, then the changes in those,
when it's "per time" and whether "in time",
that residues and moduli in integer moduli,
and "field arithmetic and a clock arithmetic
a modular arithmetic", that in _groups_,
those two groups are always singular to each
other with more than one law of large numbers,
while for example otherwise it's classical,
groups relating or not.
So, "I don't know", yet "where it _is_ and where it _isn't_",
that the quadratic sieve "draws" primes, then as
with regards to "what x^e signless or magnitude, connected
like the parabola x^2", marks on integer and lattice points
like the quadratic sieve marks the composite numbers,
then for example whether infinity is prime, usually,
or composite, and draws out, prime at infinity.
This applies to many conjectures in number theory
because most all involve infinitary expressions.
The moduli, is maybe not dense to quadratic residues,
about the square-free, a ^ (b ^ n) mod p, moduli p,
also about where "a ^ (b^n)" and "a^b^n" fall out,
where I often notices that "a^b^n" falls out terms
to "a^(b^n)", when for example sign a =/= sign b.
Anyways in a catalog of sort of conjectures of
infinitary expressions, and the various models
where they are and aren't so according to whether
there is or isn't a point at infinity, for example,
here has that I can't make so much use of the
"2's-log and e's-log, when it's 2^e and e^2,
exponentiated", then has that the moduli, usually
has that in large numbers, those would be uniform
in the moduli, i.e. "in the class of residues zero mod p",
of e^(2^n) mod p, has whether larger moduli are or
aren't more likely to make quadratic residues,
whether or not the parabolic, fills out the quadratic,
for example according to whether or not there's a
point at infinity (a single point at infinity)
that is connected or not by the quadratic sieve
and always falls _in_, lower numbers what get
drawn, whether or not it fills out and there's
also a point at infinity, so that besides it's
density going to zero in the infinite, that it
also has a "non-zero density floor", which stands
in for its condition in convergence criterion condition,
whether or not there's a point at infinity.
Then, it either sort of is or isn't these those,
while it's sort of so, yet there's also whether
primes, i.e. "residues, or primes, or integral
moduli", here the most comforting step usually
being the "square-free", or that for number theorists
much applied sits in the square-free, or that's my
impression, then also for "square-free or also
some kind of log-free", then also for the existence
besides in terms, of the constants, when those would
"suffice in the same way", that the density going
down the line would tend to add up or even out.