If $n,k\in\mathbb N$, solve $2^8+2^{11}+2^n=k^2$.
23523
Two problems on number theory
103993
Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
75489
Solve $x^2$ $mod$ $23 = 7^2$
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
89705
How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
61022
Diophantine Equations : Solving $a^2+ b^2=2c^2$
119146
How to solve $n < 2^{n/8}$ for $n$?
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
97150
Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$.
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
71756
diophantine equation: $x^2 +y^2 = z^n$
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.