query: Modulus problem with need to prove
positive_passages.docid: 21250
positive_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
negative_passages.docid: 14668
negative_passages.text: complex number question involving modulus
negative_passages.docid: 139
negative_passages.text: Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
negative_passages.docid: 81267
negative_passages.text: A simple doubt in number theory problem.
negative_passages.docid: 68880
negative_passages.text: propositional calculus problem, how to prove this right or wrong?
negative_passages.docid: 110703
negative_passages.text: How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
negative_passages.docid: 22584
negative_passages.text: Can we prove that a statement cannot be proved?
negative_passages.docid: 3632
negative_passages.text: Basic number theory proofs
negative_passages.docid: 157711
negative_passages.text: Number Theory: Prove that $m | \phi(a^m - 1)$
negative_passages.docid: 93094
negative_passages.text: How do I solve this problem on maximizing sum modulo a given number?
negative_passages.docid: 114043
negative_passages.text: Prove the existence of a real number satisfying a property
negative_passages.docid: 125263
negative_passages.text: How to crack the proof
negative_passages.docid: 118955
negative_passages.text: Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus
negative_passages.docid: 22053
negative_passages.text: Modular Arithmetic - Pirate Problem
negative_passages.docid: 119582
negative_passages.text: How to select the right modulus to prove that there do not exist integers $a$ and $b$ such that $a^2+b^2=1234567$?
negative_passages.docid: 5934
negative_passages.text: How to prove floor identities?
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