query: Positive integer solution such that $7^m - 3^m$ is prime
positive_passages.docid: 68824
positive_passages.text: Show that $\frac{(3^{77}-1)}{2}$ is odd and composite
negative_passages.docid: 151036
negative_passages.text: arithmetic progression of primes
negative_passages.docid: 144851
negative_passages.text: For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
negative_passages.docid: 21874
negative_passages.text: Solve $x^3+x \equiv 1 \pmod p$
negative_passages.docid: 24988
negative_passages.text: Prove there exists $m > 2010$ such that $f(m)$ is not prime
negative_passages.docid: 10742
negative_passages.text: Powers of prime factors of a positive integer $n$ in "Mathematica"?
negative_passages.docid: 71788
negative_passages.text: Prove existence of multiplicative inverse modulo p when p is prime
negative_passages.docid: 136279
negative_passages.text: Infinitely many primes $\equiv 3 \mod 4$
negative_passages.docid: 146512
negative_passages.text: Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
negative_passages.docid: 125188
negative_passages.text: how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
negative_passages.docid: 94917
negative_passages.text: Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
negative_passages.docid: 105405
negative_passages.text: Product of three consecutive positive integers is never a perfect power
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 91451
negative_passages.text: find all positive integer $m,n$
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$