For how many pairs of positive integers n and m is the statement $mn - 8m + 6n =0$ true?
118744
Show that there are exactly 16 pairs of integers $(x,y)$ such that $11x+8y+17=xy$.
64803
Counting two ways, $\sum \binom{n}{k} \binom{m}{n-k} = \binom{n+m}{n}$
126820
How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?
83400
Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
118197
Solve $n(n+1)(n+2)=6m^3$ in positive integers
77448
$n\ge 8\,\Rightarrow\, n = 3j + 5k\ $ for $\,j,k,n\in \Bbb N$
72402
Summation of natural number set with power of $m$
27544
With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
147317
multiple choice question on number theory
112575
Finding integer solutions of $m^2-n^5 = m - n$
111938
How do I find a flaw in this false proof that $7n = 0$ for all natural numbers?