To prove $512^3+675^3+720^3$ is Composite
10767
Prove that $512^3 + 675^3 + 720^3$ is a composite number
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
143510
Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
116175
Show that $\gcd(3k+2,5k+3)=1$
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$