query: How to show that $(a \text{ } mod \text{ } m)^2 \text{ } mod \text{ } m = a^2 \text{ } mod \text{ } m$?
positive_passages.docid: 17176
positive_passages.text: Proof that $x^n \mod b = (x \mod b)^n$
negative_passages.docid: 127291
negative_passages.text: Show that $\left( \frac{q}{p} \right) \equiv q^{(p-1) / 2} \mod p$, where $\left( \frac{q}{p} \right)$ is the Legendre Symbol
negative_passages.docid: 55049
negative_passages.text: How to find the inverse modulo $m$?
negative_passages.docid: 46147
negative_passages.text: Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
negative_passages.docid: 85449
negative_passages.text: Show a,b,c congruences when $a^2+b^2=c^2$
negative_passages.docid: 10105
negative_passages.text: Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
negative_passages.docid: 106584
negative_passages.text: If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
negative_passages.docid: 144502
negative_passages.text: Showing that $A\cap B = A\setminus (A\setminus B)$
negative_passages.docid: 52354
negative_passages.text: Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
negative_passages.docid: 152039
negative_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 41895
negative_passages.text: Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
negative_passages.docid: 30752
negative_passages.text: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
negative_passages.docid: 107095
negative_passages.text: Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
negative_passages.docid: 90438
negative_passages.text: To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
negative_passages.docid: 127816
negative_passages.text: Number theory proof mod p
negative_passages.docid: 66861
negative_passages.text: Show that $11^{10} \equiv 1 (\mod 100)$
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$