All Questions
6
questions
1
vote
1
answer
89
views
Which numbers result in a chain other than $2 \to 0$?
Let $n$ be a natural number and $k$ the number of its divisors. Calculate $n-k$, then repeat this procedure by taking $n-k$ as the starting value. If you do this repeatedly, which numbers results in ...
- 409
1
vote
2
answers
577
views
What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
I saw this in quora.
What are all the
integer solutions to
$a^{b^2} = b^a$
with $a, b \ge 2$?
Solutions I have found so far:
$a = 2^4 = 16, b = 2,
a^{b^2}
= 2^{4\cdot 4}
=2^{16},
b^a = 2^{16}
$.
$...
- 108k
0
votes
2
answers
114
views
Proving the divisibility of $4[(n-1)!+1]+n$ by $n(n+2)$ in the condition of $n,n+2 \in P$ where $P$ is the set of prime numbers [duplicate]
Let $n$ and ($n+2$) be two prime numbers. If any real value of $n$ satisfies that condition, then prove that $$\frac{4{[(n-1)!+1]}+n}{n(n+2)} = k$$ where $k$ is a positive integer.
SOURCE: BANGLADESH ...
- 1,188
4
votes
13
answers
871
views
Between which two integers does $\sqrt{2017}$ fall?
Between which two integers does $\sqrt{2017}$ fall?
Since $2017$ is a prime, there's not much I can do with it. However, $2016$ (the number before it) and $2018$ (the one after) are not, so I tried ...
- 4,581
1
vote
4
answers
3k
views
Given the numerical succession 5, 55, 555, 5555, 55555... Are there numbers that are multiples of 495? If so, determine the lowest.
I get the solution (555555555555555555) by using prime factorization. But I was wondering if there is a solution using modular arithmetic.
- 45
3
votes
3
answers
281
views
$\operatorname{lcm}(n,m,p)\times \gcd(m,n) \times \gcd(n,p) \times \gcd(n,p)= nmp \times \gcd(n,m,p)$, solve for $n,m,p$?
$\newcommand{\lcm}{\operatorname{lcm}}$
I saw this in the first Moscow Olympiad of Mathematics (1935), the equation was :
$$\lcm(n,m,p)\times \gcd(m,n) \times \gcd(n,p)^2 = nmp \times \gcd(n,m,p)$$
My ...
- 153