How many integer solutions are there to the inequality $x_1 + x_2 + x_3 \leq 17$ if we require that $x_1 \geq 1$, $x_2 \geq 2$, $x_3 \geq 3$?
48108
(Probability) How many integer solutions are there to the inequality $x_1 + x_2 + x_3 \le 17$
77595
Number of solutions of $x_1 + 2x_2 + 3x_3 + \cdots + n x_n = p$
94700
Integer solutions for $x^3+2=y^2$?
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
8446
Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$
35066
Nature and number of solutions to $xy=x+y$
3030
Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
70662
How many non-negative integer solutions does the equation $3x + y + z = 24$ have?
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
108782
Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
33314
How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
31535
Solving an inequality : $n \geq 3$ , $n^{n} \lt (n!)^{2}$.
140763
How to prove that $\sum_{n=1}^{2012} \frac{1}{x_n} = 1 $ has finitely many solutions for positive integer $x_i$?
10635
diophantine equations $x^3-2y^3=1$