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 14 Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$ 14 Is memory unimportant in doing mathematics? 12 Combinatorial argument to prove the recurrence relation for number of derangements 10 Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ 8 Continuous solutions of $f(x) = \lambda \int_0^{\pi/2} \cos({x-y)}f(y)\,dy$

### Reputation (1,400)

 +10 Good problem book on Abstract Algebra +10 Combinatorial argument to prove the recurrence relation for number of derangements +10 Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$ +10 Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$

### Questions (12)

 16 How many circles are needed to cover a rectangle? 11 $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible. 10 Good problem book on Abstract Algebra 8 Difficulties with Chapter 2 in Rudin 7 Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$

### Tags (46)

 14 algebra-precalculus 10 integration × 2 14 proof-writing 10 limits × 2 12 sequences-and-series × 3 8 integral-equations 12 combinatorics × 2 8 functional-analysis 12 inclusion-exclusion 5 differential-equations × 4

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