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2 questions from the last 7 days
2
votes
1
answer
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Limit with floor sums reminiscent of the exponent of the central binomial coefficient
This problem comes from the 1976 Putnam exam.
Evaluate
$$
L=\lim_{n\to\infty} \frac{1}{n}\sum_{k=1}^n
\left(
\left\lfloor\frac{2n}{k}\right\rfloor
-2\left\lfloor\frac{n}{k}\right\rfloor
\right),
$$
...
- 23
0
votes
2
answers
360
views
Solve $[x]+[x^2]=[x^3]$
the problem
Solve $[x]+[x^2]=[x^3]$
my idea
using the fact that $ x=[x]+ \{ x \} $ we can write the equation as $x^3-x^2-x=\{x^3\}-\{x^2\}-\{x\} \in (-2,1)$ because ${x} \in [0,1)$
Now we can solve $x^...
- 539