Math-Forums » Number Theory

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Welcome to Math Forums where you can ask questions or find answers on anything related to mathematics. Discuss about Fermat's theorem, prime numbers, algebraic number theory, Euler's theorem, congruences, and modulo. You can also discuss the Modular Division Algorithm, multiplicative orders modulo powers, and Variations on Ulam.

Math-Forums » Number Theory

1M ago

Let's call a number N 'sub-perfect' if the sum of its divisors less than N is N-1. (There may be a different term for such numbers). It is easy to see that powers of 2 are sub-perfect. Does anyone know a proof or counter-example to the conjecture that all sub-perfect numbers are powers of 2 ..read more

Math-Forums » Number Theory

2M ago

I am sorry for my English.
This is a repost from one forum member from another mathematical forum. I'll try to translate it into English (as best I can). [this is a text from another person on the forum]:
Since Petrov is being quoted here, he also has a much more interesting article devoted to prime numbers: “Petrov I.B. METAREMULTION (general superficial numerical study of an interesting prime number)” Author’s article, self-publishing, 2023, 5 pp. (attached to...
Is Petrov’s “metaremultion” finite ..read more

Math-Forums » Number Theory

4M ago

My idea of proving this theorem is presented in the attacheded document. May be it is not worth your time but I was facinated by the simplicity of the proposition and devoted a good amount of time and thinking ..read more

Math-Forums » Number Theory

5M ago

Hi think I may have found a new formula for the Riemann hypothesis.
This is how you find the real side of the limit of zeta(n+bi):
https://www.desmos.com/calculator/rcyapfsmuz
Here is how you can find the imaginary side of the limit:
https://www.desmos.com/calculator/uaociu20r4
The y=a(60) on the top is your final answer, you can increase its accuracy by setting the v to a larger number or by plugging in a higher number into that y=a(60). You can check the final answer...
New formula for the Riemann Hypothesis ..read more

Math-Forums » Number Theory

6M ago

Addition, subtraction, multiplication and exponentiation modulo n are no problem.
Division modulo n (often) IS a problem since fractions are not allowed, only integers.
Normally you would calculate the answer to a modular division by calculating the multiplicative inverse of the denominator and then multiply the numerator by that inverse. (everything mod n of course)
This is perfectly okay and works fine.
My question is: is there an algorithm that gives me the answer to a modular division...
Modular Division Algorithm ..read more

Math-Forums » Number Theory

7M ago

Hey guys so I was wondering what you thought of this number Meum. I met it while talking to myself - ironically in a jail. I was trying to compute the shapes of fractal equations in my head and got a shiver down my spine.
"Why does this number show up everywhere, who are you?
"I am meum, 1.19758, I exponentiate to infinity perfectly.
Years later I found the top level equations. Apparently the value doesn't vary ..read more

Math-Forums » Number Theory

7M ago

Diagonaliztion as a process involves constructing a number that cannot possibly exist in an infinite list of numbers of a set such as the reals, then because that list was assumed to have a bijection with the naturals it concludes that a bijection is impossible. This conclusion however is flawed in that it is never tests if diagonalization will also create a new natural number not in the list of natural numbers that we can then use to continue the bijection.
Say we have a list of all...
The flaw in Cantor's Diagonalization Argument ..read more

Math-Forums » Number Theory

7M ago

The natural numbers are analogous to an infinite line with a beginning and no end. We can continue that line into the integers and it becomes infinite in two directions. A line is defined by two points, we'll denote those two points as a set {x,y}. For the natural numbers x is 1 and y is infinitely large. For the integers x is infinitely small and y is infinitely large. As such I'll denote the naturals as {1,y} and the integers as {x,y}. When we expand into the rational numbers we are...
Working on a theory of countable cardinals ..read more

Math-Forums » Number Theory

7M ago

Claim: The real numbers are countable
Proof using bijection
Create a bijection between the natural numbers > 1 and the set of all multisets of prime numbers using the definition of prime factorization and index each correspondence using the natural numbers enumerated by n.
N:n>1⇒ {M(p)}
1: 2 ⇒ {2}
2: 3 ⇒ {3}
3: 4 ⇒ {2,2}
4: …
Using a bijection between the natural numbers and the prime numbers in sequence of least to greatest, create a...
Proof of Countable Reals ..read more

Math-Forums » Number Theory

7M ago

Let the set of natural numbers be denoted by N. Let the set of real numbers between 0 and 1 be denoted by R_01. Let f be a function that maps each natural number n to a real number between 0 and 1, where f(n) is obtained by reversing the digits of n and removing any trailing zeroes. If f(n) has a repeating decimal of the form 0.999..., then increment the digit in the next highest place by 1 and remove the repeating nines. Formally, we can define f as follows:
f: N → R_01
f(n) = 0 if n = 0...
A very simple bijection between reals and naturals ..read more