[FRIAM] Tweet from MathType (@MathType)

[Jon Zingale]

ps.

Further down that twitter stream, there is a math problem presented
by the UK mathematics trust. The problem is to find the smallest prime
which divides (300^300)-1. Using the ideas in my post above we can
see that (300^300)-1 is a very large number:

136891479058588375991326027382088315966463695625337436471480190078368997177499076593800206155688941388250484440597994042813512732765695774566000999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

For those that have learned the 3's trick, we can quickly verify that 3 does
NOT divide this number because the sum of the digits here gives 6092 which
is NOT divisible by 3.

This is an example of considering the large number above to be a list
of numbers. Next, applying the Pollard Rho method, I quickly found that 7
DOES divide this number. To verify, I use a method similar to the 3's trick
(well really the same) and pop the last 9 off the list, multiply it by 2 and
then subtract it from the remaining list. This gives another really large
number, but iterating through the list eventually gives a much smaller
number that can easily be verified to be divisible by 7. Therefore the
whole number is divisible by 7. Now part of the beauty of the *div/mod*
characterization I mentioned earlier is that we can then arithmetically
define Kronecker deltas for numbers by defining functions that act
on numbers as lists, which I do here
<https://github.com/jonzingale/Haskell/blob/master/HaskellStudy/Lists/Listable.hs>
.

Techniques like this appear almost everywhere and deltas are a similar
such thing. Consider the Dirac Delta in particular. There we have a
generalized function that is tremendously useful for selecting values out
of a time-series and yet really isn't a function at all.

Jon
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