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 18 Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$ 11 Solve equations $\sqrt{t +9} - \sqrt{t} = 1$ 10 Are normal subgroups transitive? 8 Closed subsets $A,B\subset\mathbb{R}^2$ so that $A+B$ is not closed 6 Prove or disprove: If $x^T A x = 0$ for all $x$, then $A = 0$.

### Reputation (2,461)

 +5 set of all holomorphic functions is a integral domain +10 Are normal subgroups transitive? +10 What Möbius transformation maps the unit circle $\{z: |z|=1\}$ to the real axis? +15 How does $4(1+2+…+(n-1))$ equal $4(n-1)n/2$?

### Questions (18)

 9 Cantor set + Cantor set =$[0,2]$ 6 If $f^2$ is an analytic function then so is $f$ 6 Question from Artin's algebra book 4 splitting field of $(x^3-2)(x^3-3)$ over $\mathbb Q$ 4 Möbius transformations form a simple group

### Tags (44)

 29 algebra-precalculus × 3 15 group-theory × 6 25 linear-algebra × 15 10 complex-analysis × 10 24 real-analysis × 11 9 sequences-and-series × 5 18 proof-writing 9 elementary-number-theory × 3 17 matrices × 8 8 functions × 4

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