query: Which property of modular arithmetic is being used here?
positive_passages.docid: 10105
positive_passages.text: Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
negative_passages.docid: 49294
negative_passages.text: prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
negative_passages.docid: 131905
negative_passages.text: Proof for exponentiation in modular arithmetic
negative_passages.docid: 81058
negative_passages.text: Evaluate $6^{433} \pmod {21}$ and a proving question
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: 107866
negative_passages.text: How is information disclosed by modular multiplication?
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: 52483
negative_passages.text: Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
negative_passages.docid: 18767
negative_passages.text: How do you find the modular inverse of $5\pmod{\!11}$
negative_passages.docid: 114519
negative_passages.text: An elementary question regarding a multiplicative character over finite fields
negative_passages.docid: 9039
negative_passages.text: What is the best way to solve modular arithmetic equations such as $9x \equiv 33 \pmod{43}$?
negative_passages.docid: 22053
negative_passages.text: Modular Arithmetic - Pirate Problem
negative_passages.docid: 16700
negative_passages.text: Modular reduction of fractions
negative_passages.docid: 10606
negative_passages.text: Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result
negative_passages.docid: 71821
negative_passages.text: How do I derive the time complexity of encryption and decryption based on modular arithmetic?
negative_passages.docid: 89716
negative_passages.text: Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
negative_passages.docid: 118955
negative_passages.text: Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus