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Symplectic manifold topology:

https://www.ias.edu/ideas/2016/nelson-symplectic-topology

https://www.ias.edu/ideas/2016/nelson-symplectic-topology

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A method to determine the value of a natural number raised to power and also sum of series of natural number which is raised to power.

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9/21/17

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News link: (what number theory is not about);

http://www.foxnews.com/science/2017/09/15/biblical-prophecy-claims-world-will-end-on-sept-23-christian-numerologists-claim.html

http://www.foxnews.com/science/2017/09/15/biblical-prophecy-claims-world-will-end-on-sept-23-christian-numerologists-claim.html

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We can find powers by this triangle of numbers. For bottommost raw multiply by the combination NC1 where N is the number which will be raised to the power 1. Similarly the second last raw we can find the power raised to 2. Multiply the two numbers with NC1 and NC2 respectively. Similarly with the 3rd last and 4th last raw for the powers raised to 3,4...so on.

We can find the series of power

1^n + 2^n + .......m^n.

For this we should multiple the numbers to the respective number of the raw of the triangle

(N+1)C(1+1), (N+1)C(2+1), (N+1)C(3+1)....so on. Which appear as an hockey stick of Pascal triangle.

We can find the series of power

1^n + 2^n + .......m^n.

For this we should multiple the numbers to the respective number of the raw of the triangle

(N+1)C(1+1), (N+1)C(2+1), (N+1)C(3+1)....so on. Which appear as an hockey stick of Pascal triangle.

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News Link: the symbol for zero used...

https://www.newscientist.com/article/2147450-history-of-zero-pushed-back-500-years-by-ancient-indian-text/

https://www.newscientist.com/article/2147450-history-of-zero-pushed-back-500-years-by-ancient-indian-text/

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