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Results tagged with elementary-number-theory
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user 966209
For questions on introductory topics in number theory, such as divisibility, prime numbers, gcd and lcm, congruences, linear Diophantine equations, Fermat's and Wilson's theorems, the Chinese Remainder theorem, primitive roots, quadratic congruences, quadratic number fields, Pell's equations, and related topics.
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Are there infinitely many $n\in\mathbb{N}$ which equals the sum of square of its smallest $k...
For $n\in\mathbb{N}$ , let $d_1<d_2<…<d_m$ be all divisors of $n$, where $d_1=1$, $d_m=n$, and $m=\tau(n)$ is the number of (positive) divisors of $n$ .
Questions: There are two questions related with …
- 261
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Binomial coefficients sum $\sum_{k=1}^{n} \frac{1}{k}\binom{2k}{k}$ when $n>1$, $p=2n+1$ is ...
For a prime $p>3$, assume $n=\frac{p-1}{2}$.
Question: Is it true that $\sum_{k=1}^{n} \frac{1}{k}\binom{2k}{k}\equiv0\text{(mod}$ $p)\,?$
A MATLAB program shows that there is no counterexample when $ …
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