Description:
Mathematical discussions and pursuits.
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Statistics with sample standard deviation.
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Hello teacher~ The standard deviation of the distribution of the sample means is equal to the actual population standard deviation divided by the square root of n. Namely, sigma(X_bar) = sigma / [sqrt(n)] As a practical matter, since we rarely know the population standard deviation, we will use the sample standard deviation in class to estimate... more »
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visualizing the distribution of primes
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Hi. Here you can find a graphic created in photoshop to see how primes are distributed among a kind binary square configuration of non-negative integers: [link] This webpage also offers nice visual patterns related to primes and provided some inspiration:... more »
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What is the next Prime that is 3 mod 4 from this one?
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Hi, I have this prime (base 10): 104438888141315250667960271984 652954583126906099213500902258 875644433817202232\ 269071044404666980978393011158 573789036269186012707927049545 451721867301692842\ 745914600186688577976298222932 119236830334623520436805101030 915567415569746034\ 717694639407653515728499489528 482163370092181171673897245183 497945589701030633\... more »
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Mr.Putin’s note about the USA-Georgia
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Dear Newsgroup: In the BBC today we have: [link] Putin blames US for Georgia role Then further written: “ Russian Prime Minister Vladimir Putin has accused the US of provoking the conflict in Georgia, possibly for domestic election purposes.” I would say his statement is theoretically correct (possibly Israel is... more »
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An Interesting Congruence
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Hello group, The following congruence, sum(j = 0 to j = greatest int in (n-1)/2) (n C (2j+1)) * (a^j) is congruent to 0 mod 2^(n-1) whenever n > 0 and a is congruent to 1 mod 4. is true and I can prove it. Of course it doesn't say much when n = 1, and when a = 1 it just reflects the fact that the sum is equal to and hence obviously... more »
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Japan
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Dear Newsgroup: In order to more strengthen the position of Japan in Asia, I would like to suggest the following: 1-Japan will have Bahrain as its sole colony. This will hopefully support energy issues of not only Japan but also its colonies (in the Asia) as those mentioned as well as those will be named in the future.... more »
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Solutions of an equation
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Consider the following equation under the given conditions. (x^2 + y^2)^k = M (1) conditions: M is an integer > 1, prime k > 5 x and y are to be determined. My assertion: x and y can only be of the following forms: 1. both x and y are rational 2. x = a + sqrt(b) and y = a - sqrt(b); a is rational, b need not be a... more »
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Solution of an algebraic equation
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Hi, I would like to know how to solve: x^m -ax + a - 1 = 0 with a >1, m>1, a real and m integer. An obvious real solution, for each (a,m) satisfying the given constraints is x=1. I would like to find at least another real solution, for each (a,m), if it exists, or otherwise determine which additional constraints must be imposed on... more »
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Iran And Syria
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Dear Newsgroup: I would like to summarize the many phases of recommendations I have already provided for the Middle East Area: 1-The city of Jerusalem will be a colony of Turkey. 2-Saudi Arabia will be partitioned between the nations Jordan (having the city of Mecca), Egypt and Turkey (the rest). 3-Dubai will be a colony of Italy and Spain.... more »
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