How to count number of positive solutions of an equation $x_1 + x_2 +...+ x_n = s$ where $0 < x_i \le c $.
24036
extended stars-and-bars problem(where the upper limit of the variable is bounded)
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
51804
How to show that a root of the equation $x (x+1)(x+2) ....... (x+2009) = c $ can have multiplicity at most 2?
9490
Let $(1+x+x^2)^n=a_0+a_1x+a_2x^2+\cdots+a_{2n}x^{2n}$ be an identity in $x$. Find $a_0 +a_2 +a_4+ \cdots +a_{2n} $ in terms of $n$
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
48268
How many $\alpha \in S_n$ are such that $\alpha^2 = 1$?
95494
Number of solutions of an arithmetic function's equation
1001
Number of integer solutions of $x^2 + y^2 = k$
91003
Prove that equation has exactly 2 solutions
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
146126
Infinite positive integer solutions of the equation: $x^2+x+1=(y^2+y+1)(n^2+n+1)$
16660
Prove that any positive number has an $n$th root
105347
How many nonnegative integer solutions are there to the pair of equations $x_1+x_2+…+x_6=20$ and $x_1+x_2+x_3=7$?
95409
Find no. of non negative integer solutions of $a+2b+3c = 200$
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
946
How to find solutions of linear Diophantine ax + by = c?
91451
find all positive integer $m,n$