Finding 8 Numbers with phi(n) = 240

  • Thread starter Thread starter AH05
  • Start date Start date
  • Tags Tags
    Numbers
AH05
Messages
4
Reaction score
0
Find eight different numbers n with phi(n) = 240.



phi(n) = the number of positive integers less than or equal to n, that are relatively prime to n.
 
Physics news on Phys.org
Surely you are aware that you must show what you have tried yourself before anyone can give suggestions?
 
12^12 = (3^12)(2^24)

phi(12^12) = phi(3^12) * phi(2^24) = 2^(24-1) * (2-1) *3^12 *(3-1)
= 2^23 * 3^12 * 2 = 2^24 * 3^12
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
584
Copeland-Erdős number
Replies
10
Views
2K
Each integer n>11 can be written as the sum of two composite numbers?
Replies
7
Views
4K
An integer n>1 is square-free if and only if?
Replies
13
Views
4K
The only prime of the form n^3-1 is 7?
Replies
2
Views
4K
Finding the nth roots of a complex number
Replies
23
Views
340
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
Replies
3
Views
2K
Find all odd n such that n|3^{n}+1
Replies
9
Views
3K
U(n) as an External Direct Product
Replies
11
Views
2K
Any integer of the form ## 8^n+1 ##, where n##\geq##1, is composite?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top