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Greetings in the Marsday ... the day of the Love of God ... the day of ... Koot Hoomi, the Lord of Pink Ray of Love ...
I, Giovanni ... discover the Millenium Problems ... from Italy ... and when I return for a Holiday in Caracas, Venezuela ... A Holiday that takes me two years ... no one in Math Department in Caracas ... know about.
Is more than evident that ... I, Giovanni do not teach in any University ... and last courses I dictate were related to Computer Science in Caracas ...
But let us do not talk about ... Caracas and me ... but about ... the Millenium Problems.
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The Millenium Problems are a small group of Problems ... to measure the border of Mathematics ...
A Great Business Man ... may be lover of Mathematics ... invest some Million dollars to create the Clay Math Institute. His name was Landon T. Clay
Click to read more about the Problems ...
The Riemann Hypothesis claim that all zeros of the complex valued function ...
ζ(s) = 1 + 1/2^{s} + 1/3^{s} + 1/4^{s} + ...
called the Riemann Zeta function or all interesting solutions of the equation
ζ(s) = 0
lie on a certain vertical straight line.
There are relations between Quantum Physics and the Riemann Hypothesis you can find in the book ...
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The P vs NP Problem relates the problems ... NPcompleteness which means nondeterministic polynomial time vs P, or problems which can be solved in Polynomial Time.
Now some days ago we talk about Euler ... and the "change problem" ... or how many ways we can change 1 dollar and/or 1 Euro.
Are you interested to know Euler Solution to the Change problem? ... Also Euler connect Prime Distribution numbers with Zeta Function ...
This problem ... "how to change" or "change problems" belong to a more sophisticated problem called "Partitions" that in the most elementary mode relates, in how many ways ... we can add ... a number.
If we consider 6, by example ... like Euler did in Chapter 16 ... of his book, we got ...
6=6 ... 6=3+1+1+1 ... 6=5+1 ... 6=2+2+2 ...
6=4+2 ... 6=2+2+1+1 ...
6=4+1+1 ... 6=2+1+1+1+1 ...
6=3+3 ... 6=1+1+1+1+1+1
6=3+2+1
6 have 11 different ways to be written ...
Now, the mode Euler solve this ... is quite interesting ... he consider the multiplication of series and ... the coefficient of the term ... very related to what today we call Combinatoric Coefficient or related to Pascal Triangle.
Now the point ... to honor Euler is the fact ...
We hope you got ... Euler idea ...
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To begin to conclude this first journey ...
We can say ... Ramanujan ... The Genius from India ... worked on Partitions ... like Godfrey Harold Hardy and also together ... Erdos too ...
Now ... this problem seems "simple" but in its Highest evolution ... has been declared ... NP ... and this is the first problem we discuss a little bit ...
I, Giovanni ... complete the High School at the age of sixteen ... and learn to program the computer with some assistance in that age. Also my first spiritual experience was at the age of sixteen ... then I enter in Science Faculty studying Physics and then change to Mathematics ... In Italy, I got the Italian degree ... working in CS (Computer Science) ...
But ... like a Philosopher I know ... I have too much to learn ...
At the age of sixteen ... aware I am studying what is consider a NP problem ... I read ... "Basic Programming" by john kemeny and thomas kurtz.
Well, at page 60 ... You can read ...
Anyone can access a Machine to run BASIC ... most simple than BASIC ...
Now, the posted question on Feb 21, 2018
 In how many ways you can change 1 US$ ... with coins of cents, nickels, dimes, quarters and halfdollar. (See G. PolyaG. Szego Problems and Theorems in Analysis I)
 In how many ways you can change 1 Euro ... with coins of 1 cent, 2 cent, 5 cent, 10 cents, 20 cents and halfeuro ...
can here be solved:
The lines 90 and 91 ... are extremely important.
We read:
The first number 5 represents the maximal number of coins ... to change 20¢.
The first 3 ... represent how many different types of coins will be used ... 3 types ... 1¢, 5¢ and 10¢.
We note the first run ... the last number is 9 ... (See the first run on the figure above on the right).
This number 9 ... represent in how many ways we can change 20¢ with coins of 1¢, 5¢ and 10¢.
If we now change ... the DATA to ...
 DATA 6,100
 DATA 6,1,5,10,25,50
This means we will change 100¢ ... or 1US$ ... and the result is 292.
For the Euro we need to change ... the second line of DATA ... as follow:
DATA 6,1,2,5,10,20,50
What is the result? ...
Thanks,Giovanni A. Orlando PS. Also at the age of sixteen ... I enter also to work in Bank ... but, I change my horizons ... and they continue to change.
