query: How can I simplify $(n\,\mathrm{ mod }\,b^{k+1})\,\mathrm{ mod }\, b^k$?
positive_passages.docid: 29204
positive_passages.text: $a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
negative_passages.docid: 126105
negative_passages.text: Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
negative_passages.docid: 43683
negative_passages.text: Finding Inverse of 2 (mod m)
negative_passages.docid: 101057
negative_passages.text: Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
negative_passages.docid: 74512
negative_passages.text: How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
negative_passages.docid: 74294
negative_passages.text: How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
negative_passages.docid: 116722
negative_passages.text: Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
negative_passages.docid: 19285
negative_passages.text: simplifying $ (h^2_2-h^2_3)\over ({1\over h_3})-({1\over h_2})$
negative_passages.docid: 139659
negative_passages.text: Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
negative_passages.docid: 30518
negative_passages.text: Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
negative_passages.docid: 39969
negative_passages.text: Algorithms for computing multiplicative order modulo $n$
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion
negative_passages.docid: 19071
negative_passages.text: solution set for congruence $x^2 \equiv 1 \mod m$
negative_passages.docid: 51679
negative_passages.text: Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$
negative_passages.docid: 87397
negative_passages.text: Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
negative_passages.docid: 118024
negative_passages.text: Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$
negative_passages.docid: 111555
negative_passages.text: Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$