5 Prove Positivity of a Function Involving $\log$. 4 can't find global minimizer from Lagrange Multiplier Rule 3 Find all natural solutions that satisfy $2^𝑥 + 3^𝑦 = 𝑧^2$ 3 Inequality of functions 3 Complex Numbers and the Norm

### Reputation (1,555)

 -2 Show that $3n^4+3n^2+1$ is never a perfect square +8 A better-than-trial-and-error algorithm to compute $a,b$ with $a^2+b^2\equiv -1\pmod{p}$ +38 Computing $a,b$ with $a^2+b^2\equiv -1\pmod{p}$ +10 can't find global minimizer from Lagrange Multiplier Rule

### Questions (21)

 7 Why is $\frac{1}{10}\left(\frac{9}{10}+\frac{8}{9}+\dots+\frac{1}{2}\right)\approx \frac{\sqrt{2}}{2}$? 4 Elementary Geometry: Prove that ABCD is a tangential quadrilateral! 3 Computing $a,b$ with $a^2+b^2\equiv -1\pmod{p}$ [duplicate] 3 Prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+ca}{1+c}\geq 3$ 3 Prove that a sequence is a permutation of the natural numbers

### Tags (89)

 22 calculus × 12 6 geometry × 16 15 real-analysis × 8 5 proof-verification × 5 13 inequality × 9 5 sequences-and-series × 5 7 algebra-precalculus × 7 5 complex-numbers × 3 7 optimization × 3 5 functions × 2

### Bookmarks (1)

 8 Solving a scary looking cubic by hand