query: Find and prove a formula for 1mod3 ∩ 1mod7
positive_passages.docid: 27850
positive_passages.text: Find and prove a formula for $1\pmod{3}\cap 1\pmod{7}$.
negative_passages.docid: 120571
negative_passages.text: What does it mean $a \;\text{mod}\; 1$?
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion
negative_passages.docid: 100303
negative_passages.text: A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
negative_passages.docid: 158684
negative_passages.text: How to solve and see resolution of $13^{53} \pmod 7$ using Fermat little Theorem?
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: 94965
negative_passages.text: Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$
negative_passages.docid: 39373
negative_passages.text: How can I calculate $24^{33} \bmod 80$
negative_passages.docid: 29204
negative_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: 147665
negative_passages.text: $a_1=3;\ a_{n+1}=3^{a_n}$; find $a_{2004}\bmod100$
negative_passages.docid: 96535
negative_passages.text: Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?
negative_passages.docid: 68252
negative_passages.text: Chinese Remainder Theorem solvability for non-coprime moduli
negative_passages.docid: 26301
negative_passages.text: Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
negative_passages.docid: 39969
negative_passages.text: Algorithms for computing multiplicative order modulo $n$
negative_passages.docid: 21476
negative_passages.text: Modular Exponentiation 3^5^7
negative_passages.docid: 10105
negative_passages.text: Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
negative_passages.docid: 144067
negative_passages.text: calculating $a^b \!\mod c$