query: Let p>5 be the prime number. Prove that the expression $p^{4} - 10p^{2} +9$ is divisible by $1920$
positive_passages.docid: 146203
positive_passages.text: if p is prime then 1920 divides $p^4-10p^2+9$
negative_passages.docid: 95141
negative_passages.text: $n^5-n$ is divisible by $10$?
negative_passages.docid: 73515
negative_passages.text: Primes Number Theory
negative_passages.docid: 15348
negative_passages.text: prime divisor of $3n+2$ proof
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 10425
negative_passages.text: Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
negative_passages.docid: 82358
negative_passages.text: How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
negative_passages.docid: 26336
negative_passages.text: Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
negative_passages.docid: 56760
negative_passages.text: Prove by induction that an expression is divisible by 11
negative_passages.docid: 54359
negative_passages.text: Odd Primes Problem Proof
negative_passages.docid: 63893
negative_passages.text: Prime dividing the binomial coefficients
negative_passages.docid: 101927
negative_passages.text: Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$.
negative_passages.docid: 6561
negative_passages.text: Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.
negative_passages.docid: 136856
negative_passages.text: Diophantine equation with a prime number
negative_passages.docid: 76282
negative_passages.text: Prime number expressible as $2^2+3^3+5^5+7^7+11^{11}+\cdots$
negative_passages.docid: 13478
negative_passages.text: Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
negative_passages.docid: 136947
negative_passages.text: Simple Mersenne prime divisibility proofs