Count the numbers of integer solutions of the ecuation $x_1 + x_2 + x_3 + x_4 = 21$
38541
How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$?
94105
Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.
63194
Find all integer solutions to $x^2-2y^2=1$
105347
How many nonnegative integer solutions are there to the pair of equations $x_1+x_2+…+x_6=20$ and $x_1+x_2+x_3=7$?
67899
Integer squares of the form $x^4+x^3+x^2+x+1$
106896
Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
146491
Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
112575
Finding integer solutions of $m^2-n^5 = m - n$
114379
Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
144260
Solve recurrence relation $a_n = 3 a_{n - 3} + a_{n-1} + 2 n$
142978
combinatorics: sum of product of integer compositions
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
42360
Find the number of solutions of $a_0+a_1+a_2=17$ if $2\le a_0\le 5$, $3\le a_1\le 6$, $4\le a_2\le 7$.
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
90830
Solve the integeral equation (C.S.I.R)
144863
Finding integer solutions to $y^2=x^3-2$