If n > 1 is an integer and x $$\ne$$ 0, then (1 + x)ⁿ $$-$$ nx $$-$$ 1 is divisible by

If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2 k}$$ is equal to

The coefficient of $$a^{10} b^7 c^3$$ in the expansion of $$(b c+c a+a b)^{10}$$ is

The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is