query: Solving the equation $1! 3! 5! ... (2n-1)! = m!$, via a combinatorial method
positive_passages.docid: 26087
positive_passages.text: Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$
negative_passages.docid: 142900
negative_passages.text: Find all positive integers a,b,c to the equation a!b!= a!+b!+c!
negative_passages.docid: 20705
negative_passages.text: On equations $m^2+1=5^n$
negative_passages.docid: 55100
negative_passages.text: The positive integer solutions for $2^a+3^b=5^c$
negative_passages.docid: 5801
negative_passages.text: Combinatorial proof help
negative_passages.docid: 61871
negative_passages.text: Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$
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: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 9920
negative_passages.text: $(n^2 - 1)!$ is a multiple of $(n!)^n$
negative_passages.docid: 118197
negative_passages.text: Solve $n(n+1)(n+2)=6m^3$ in positive integers
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 1139
negative_passages.text: Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
negative_passages.docid: 18903
negative_passages.text: Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
negative_passages.docid: 114996
negative_passages.text: $x+y+z=n$. Finding the number of solutions.
negative_passages.docid: 109706
negative_passages.text: Fast way to come up with solutions to $x(x-1)(x-2)(x-3)=1$?
negative_passages.docid: 87320
negative_passages.text: Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially