Show that there are infinitely many positive integers $N$ that cannot be written in the form $a^n+b^n+c^n$
53156
Infinitely many numbers not expressible in the form $a^n+b^n+c^n$
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
28099
Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
47162
Proving there are infinitely many primes of the form $a2^k+1.$
145558
Prove that $2^n+3^n $ is never a perfect square
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
5287
Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
139826
arbitrary large finite sums of an uncountable set.
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
129163
Showing that every positive integer can be represented in this form