Let $t_n$ denote the $n$th triangular number. For what values of $n$ does $t_n$ divide $t_1^2+t_2^2+ \cdots +t_n^2$
69858
Congruence Equation $3n^3+12n^2+13n+2\equiv0,\pmod{2\times3\times5}$
14306
What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$
94983
Can an odd number $n$ divide $2^n-1$?
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
17766
Find $n^{th}$ term of $\frac23,\frac35,\frac58,\frac8{13}\dots$
30595
If $t_n=\frac{1}{2n+1}-\frac{1}{2n+2}+\frac{1}{2n+3}-\frac{1}{2n+4}+\cdots +\frac{1}{4n-1}-\frac{1}{4n}$. Find $\lim_{n \to \infty} nt_n$
95862
Prove that $t_{n-1, \alpha/2}$ is strictly decreasing in $n$
156376
Find the values of $n$ that make the fraction $\frac{2n^{7}+1}{3n^{3}+2}$ reducible.
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
116360
Sum of n-th roots of unity
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
22573
Volume of $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$
148745
Determine if a number is the sum of two triangular numbers.
10920
$\delta_2(n)$ the sum of the squares of the positive divisors of $n$.