query: Why is $P^{ed} \bmod N = P^{1} \bmod N$ if $e$ and $d$ are modular inverses of $\phi(N)$.
positive_passages.docid: 43152
positive_passages.text: Why do we use Φ while calculating the encryption key in RSA method?
negative_passages.docid: 61860
negative_passages.text: Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
negative_passages.docid: 93820
negative_passages.text: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
negative_passages.docid: 12636
negative_passages.text: Product Rule for mod operator: $ ab\bmod p = ((a\bmod p)(b\bmod p))\bmod p$
negative_passages.docid: 20161
negative_passages.text: Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
negative_passages.docid: 94855
negative_passages.text: Prove if a (mod n) has a multiplicative inverse, then it's unique
negative_passages.docid: 26233
negative_passages.text: $[K(\zeta_n):K]=\phi(n)$?
negative_passages.docid: 55049
negative_passages.text: How to find the inverse modulo $m$?
negative_passages.docid: 23153
negative_passages.text: $\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
negative_passages.docid: 34430
negative_passages.text: Why does $(\frac{p-1}{2}!)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$?
negative_passages.docid: 91935
negative_passages.text: If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
negative_passages.docid: 78852
negative_passages.text: If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
negative_passages.docid: 43683
negative_passages.text: Finding Inverse of 2 (mod m)
negative_passages.docid: 136804
negative_passages.text: Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
negative_passages.docid: 53915
negative_passages.text: prove that $a \equiv b \mod m$ is an equivalence relation on the integers
negative_passages.docid: 133238
negative_passages.text: Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
negative_passages.docid: 4972
negative_passages.text: Mod of numbers with large exponents [modular order reduction]