Find all positive integers $n$ such that $\phi(n) + \tau(n) > n$.
75516
Relatively Prime Numbers and Number of Divisors of n
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
12976
Prove $\displaystyle\lim_{n\to\infty}\phi(n)=\infty$.
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
104982
Determine $\phi(2^{399}+1)$
27069
sum of all positive integers less than $n$ and relatively prime to $n$
149489
30 positive integers
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
158124
Sum of all the positive integers problem
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
41784
Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.
4530
For which natural numbers are $\phi(n)=2$?
64336
Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$