Find $x$ and $y$ such that $\binom{100}{0}+2\binom{100}{1}+4\binom{100}{2}+\cdots+2^{100}\binom{100}{100}=x^{y}$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
105416
How can I find an inverse to the Binet formula?
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
106441
Find the value of $\binom{2000}{2} + \binom{2000}{5} + \binom{2000}{8} + \cdots \binom{2000}{2000}$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
73716
Let $x,y,z>0$ and $x+y+z=1$, then find the least value of ${{x}\over {2-x}}+{{y}\over {2-y}}+{{z}\over {2-z}}$
29876
Find the number of triples $(x,y,z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$
126214
Multiplying Binomial Terms
28936
Proving equation with binomial coefficient
139474
Solving system of Congruences with Two Variables (x and y)
105226
How to solve this equation manually: $(x^2+100)^2=(x^3-100)^3$?
17741
Quick way to solve the system $\displaystyle \left( \frac{3}{2} \right)^{x-y} - \left( \frac{2}{3} \right)^{x-y} = \frac{65}{36}$, $xy-x+y=118$.
53725
Factor $(x+y)^4+x^4+y^4$
131326
How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
157552
Find the coefficient of $x^n$ simply by using binomial theorem