Conjecture no.45: Is there are infinitely many Lucas Sequences that have only finitely many triangular number terms in them https://en.wikipedia.org/wiki/Lucas_sequence
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A curious identity I rediscovered!
Sin(x)^2 + Cos(x)^2 = 1 for all rational numbers x. I discovered this while punching random characters on my calculator. A natural generalization is to generalise this identity to the Gaussian Integers. It would be interesting to see whether there only finitely many solutions to the equation when constrained to the Gaussian Integers and i …
My proof for P=NP draft three
Please realize that this is a draft proof. The existence of a unary decision problem that is NP Complete – A Proof Sketch By: Nunghead Abstract: We will establish that there exists a decision problem encoded in unary[1] that is NP-Complete as the main result of this paper. Definition 1.0(Strongly-NP Complete)[2] A strongly …
A slide presentation to explain the basics of Complexity Theory.
The slide presentation I will link below is to explain P and NP to a general audience. It is written at a somewhat beginner level. If you need to understand more about this , feel free to comment. Here are the slides for my talk on the topic. Suggestions for further reading would by Fortnow, …
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Some other interesting series
The first such series we shall consider is the series generated by the formula 1/8(2x+1)^2 +7 This series generates a very similar series to the triangular number i.e the difference between consecutive terms is equal to 1m. Some terms are 1, 2 , 4 , 7, and so on… Indeed, if we subtract one we …
A good approximation for the square root of three.
A good approximation for the sqrt(3) is the fraction 730081/421512 correct to five decimal places. Thank you, Nunghead
Another interesting series of numbers.
What is the pattern in the series: 2,8,20,38,62, … The pattern is that the difference of any two numbers is equal to a multiple of six. What is the formula for generating the nth such number? The formula is 1/2(x^2+1) + 1/4(x^2+3) Thank you, Nunghead
An interesting series of numbers.
I discovered a interesting series of numbers, do tell me if you see the pattern in them. 1, 5, 13, 25,41,61,85, 113, … The pattern is that the difference of any two terms is equal to a multiple of four. Now, another challenge for you is to find the formula that generates the nth such …
My proof of P vs NP variant two
DISCLAIMER:(Read This NOW Before you read my Proof!){I cannot emphasize this!}Please do recognize that this is very tentative work. I would like you to read it with caution but not skepticism. This is also presented in an unadulterated fashion as this is my second draft and so constitutes my second variant If you do not …
My proof for P vs NP Draft One, Variant One
DISCLAIMER:(Read This NOW Before you read my Proof!){I cannot emphasize this!} Please do recognize that this is very tentative work. I would like you to read it with caution but not skepticism. This is also presented in an unadulterated fashion as this is my first draft and so constitutes my first variant If you do …
Continue reading “My proof for P vs NP Draft One, Variant One”
My Mathematics work and other extraneous diversions 