Infinitely pairs of positive integers such that $1+2+\cdots+k = (k+1)+(k+2)+\cdots+N$
60902
Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
158124
Sum of all the positive integers problem
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
8446
Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
98468
Are there infinitely many primes of the form $n!+1$?
78309
On an expansion of $(1+a+a^2+\cdots+a^n)^2$
146439
Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$
47162
Proving there are infinitely many primes of the form $a2^k+1.$
21791
Show that $\sum\limits_{k=1}^\infty \frac{1}{k(k+1)(k+2)\cdots (k+p)}=\frac{1}{p!p} $ for every positive integer $p$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
129163
Showing that every positive integer can be represented in this form
94575
Inductive proof that there are infinitely many pairs of consecutive powerful integers?
57275
On the primality of integers of the form $p^2+k$
23866
Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?