How to prove $\pi^3<3^\pi$ without using explicit value of $\pi$?
22767
How to prove $3^\pi>\pi^3$ using algebra or geometry?
100568
Showing $\gamma < \sqrt{1/3}$ without a computer
51314
How to prove that a complex number is not a root of unity?
46353
Proof that $\cos(\pi/3)=1/2$
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
67527
Proof by Induction that $3^n ≥ 1+2^n$
30783
Prove inequality $n<3^n$ using mathematical induction
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
136894
Reference request: Clean proof of Fermat's last theorem for $n=3$.
41191
How to prove this $\pi$ formula?
136721
Absolute value of a complex number proof
158066
Prove $2^{1/3}$ is irrational.
65300
Why is $\pi$ irrational?
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
111267
Prove that: $2^a+3^b<3a+4b$