Tagged Questions
9
votes
3answers
319 views
Yitang Zhang: Prime Gaps
Has anybody read Yitang Zhang's paper on prime gaps? Wired reports "$70$ million" at most, but I was wondering if the number was actually more specific.
EDIT$^1$:
Are there any experts here who can ...
9
votes
2answers
49 views
Origin of well-ordering proof of uniqueness in the FToArithmetic
In the Appendix to Ivan Niven's book "Numbers: Rational and Irrational", he proves the Fundamental Theorem of Arithmetic (FToA) without using Euclid's Lemma that if a prime divides a product, then it ...
5
votes
1answer
138 views
A question on Paul Erdős's research on Egyptian fractions
A good day to everyone!
I have a (somewhat) intriguing question regarding Paul Erdős's papers on Egyptian fractions (e.g., his 2nd paper during his mathematical career was about this topic).
My ...
3
votes
3answers
315 views
Is there a text that provides the proof of Fermat's Last Theorem?
I know that professor Andrew Wiles discovered his proof of Fermat's Last Theorem in 1995. One of my friends is looking for a text which provides his proof. I know that the proof is very complicated ...
-1
votes
4answers
239 views
The facts about $\varphi$ [closed]
A lot of people believe there is something special about the number $\varphi= \frac {1+ \sqrt5}{2}$.
However, I can only think of cultural explanations for looking at each property of $\varphi$ as ...
4
votes
2answers
117 views
Plato's Disc of Gold
In the book Mathematical Cranks, Underwood Dudley describes the following problem on page 36:
Dear Archimedes,
Your problem is solved but:-- About twenty years ago he lived on Crete and was ...
3
votes
1answer
126 views
Early history of lower bounds on the prime counting function
Let $\pi (x)$ be the number of prime numbers less than or equal to $x$.
Euclid's proof of the infinitude of primes gives a horrible lower bound of the type $ \pi (x)>> \sqrt{\log{x}} $. ...
1
vote
1answer
97 views
History of the study of rational points on the circle
What is the first known instance of a mathematician parameterizing rational points on the unit circle by the slopes of rational lines going through a rational point on the circle?
4
votes
1answer
110 views
Nagura's paper--can we substitute for the original upper bound?
This question concerns two results about primes. The first is J. Nagura's 1952 result, that there is a prime on the interval $[x, (1+1/5)x] $ for $x> 2103,$ which depends on the result derived ...
14
votes
0answers
268 views
Definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel
There is a remark one can find in various books or survey articles (e.g., page 49 of Helmut Koch's "Number Theory: Algebraic Numbers and Algebraic Functions") saying Dirichlet figured out a proof of ...
9
votes
3answers
370 views
History of elliptic curves
In one sense elliptic curves are a rather modern object as some of its properties have been studied only in the last century or so. But in another sense there are a very classical object for studying ...
1
vote
1answer
119 views
Which automata recognise the algebraic numbers?
I am reading historical stuff on the algebraic and transcendental numbers. Descartes, in his Geometry, excluded all curves not expressible as algebraic equations. Later, Leibniz called such curves ...
2
votes
2answers
373 views
Can somebody simply explain Wilson's theorem (for a 13 year old)
I am Rohan Kapur. This is my first time posting on the Mathematics site, although I am quite active on StackOverflow, the programming site.
I am doing a Islamic Maths assignment at the moment for ...
9
votes
1answer
376 views
ancient concepts and modern concepts
Is there an extant published expository account, comprehensible to all mathematicians, of the conceptual differences between ancient Greek mathematical concepts and modern ones?
I have in mind things ...
2
votes
1answer
237 views
Reference request for “Weierstrass equation” and “Weierstrass normal form”
I would like to know more about the history of the widely used terms "Weierstrass equation" and "Weierstrass normal form", as they appear in the theory of elliptic curves. When were these terms first ...
2
votes
1answer
66 views
Chebyshev/Tchebycheff's results concerning $\phi(x)$.
The book "A SOURCE BOOK IN MATHEMATICS" has a great collection of mathematical papers. On of the is Chebyshev's Memoir on "The Totality of Primes Less Than a Given Number."
The book states that
...
-1
votes
1answer
218 views
Euler's Choice and Riemann's Oversight?
Euler's Choice:
When Euler crafted the zeta function, he knew that $\zeta(1)$ diverged, so he made $\zeta(1)$ undefined.
When he crafted the zeta generating function using the Bernoulli numbers, ...
5
votes
3answers
679 views
Proving Fermat's Last Theorem for n=3 using Euler's and Lamé's approach?
Euler and Lamé are said to have proven FLT for $n=3$ that is, they are believed to have shown that $x^3 + y^3 = z^3$ has no nonzero integer solutions. According to Kleiner they approached this by ...
9
votes
3answers
269 views
Fibonacci numbers modulo $p$
If $p$ is prime, then $F_{p-\left(\frac{p}{5}\right)}\equiv 0\bmod p$, where $F_j$ is the $j$th Fibonacci number, and $\left(\frac{p}{5}\right)$ is the Jacobi symbol.
Who first proved this? Is there ...
0
votes
2answers
277 views
Fermat's proof of his last theorem? [closed]
I have discovered a truly marvelous proof of this, which this margin
is too narrow to contain
Wiles himself stated that his proof could not have been the same proof that Fermat had come up ...
0
votes
1answer
286 views
Resurrection of my Tamagawa numbers Question, to understand the Formulation of BSD
My previous question was closed very badly for asking the broad and deep things, so I now understand the consequences of asking such questions, so I refrain from asking such questions, so this is not ...
3
votes
1answer
76 views
Counting bases to which numbers are pseudoprime
Let $n=p_1^{a_1}\cdots p_k^{a_k}$ be an odd composite. Then the number of bases $1\le b\le n-1$ for which n is a strong pseudoprime is
$$
\left(1 + \frac{2^{k\nu}-1}{2^k-1}\right) ...
8
votes
2answers
328 views
What's the history of the result that $p_{n+1} < p_n^2$, and how difficult is the proof?
In Edsger Dijkstra's monograph "Notes on Structured Programming", he describes a simple imperative program for generating an array of the first $n$ primes. For each prime $p_n$, it finds the next ...
7
votes
1answer
402 views
Fermat's Last Theorem: implications (there is no new proof)
I am not experienced in Number Theory but what I know is that some results of this filed are applicable in other areas, e.g. algebra. For sure FLT made (and makes) people be interested in Number ...
10
votes
1answer
315 views
Fibonacci, compositions, history
There are three basic families of restricted compositions (ordered partitions) that are enumerated by the Fibonacci numbers (with offsets):
a) compositions with parts from the set {1,2} (e.g., 2+2 = ...
32
votes
8answers
2k views
Is zero odd or even?
Some books say even numbers start from two but if you consider the number line concept, I think zero should be even because it is in between -1 and +1 (i.e in between 2 odd numbers). What is the real ...
4
votes
2answers
385 views
Politics of the Adelics
The adelics seem counter-intuitive. I wonder how they came up originally, and what was the immediate reward for introducing them. What was the politics of introducing the adelics into mathematical ...
