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Results tagged with nt.number-theory
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user 520102
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
2
votes
0
answers
212
views
Question on digital sum of the square of $n$
If we set $f(n)=$ the digital sum of $n$，for example, $f(2024)= 2+0+2+4= 8$.
Are there any $n>375501$ in solutions to the equation $f(n^2)=9,$ except $n=10k$, $n=10^a+10^b+1$, $n=5 \cdot 10^a+1$ or $n …
- 321
3
votes
Six consecutive positive integers with certain shape
With the analysis from Stanley, Joachim and Max Alekseyev, maybe I can solve my question now.
Because two different integers with the form 4k+2 can not appear in these six numbers, when modulo 4, they …
- 321
4
votes
0
answers
117
views
Do all nonnegative integers appear in A051521?
For every positive integer $n$, $\tau(n)$ is the number of divisors of $n$. If we list the ratio of each positive integer $n$ to $\tau(n)$，they form a rational sequence
1,1,3/2,4/3,5/2,3/2,…
Because $ …
- 321
12
votes
4
answers
1k
views
Six consecutive positive integers with certain shape
Are there 6 consecutive positive integers, where each of them is a square or the product of a prime and a square ?
If they exist, one of those six integers A will be the product of 2 and a square of a …
- 321