Mathematics - Binomial Theorem Question with Solution | TestHub

II is true. Since $(1+x{)}^{31}\equiv 1+x^{31}(\mathrm{mod}31)$, comparison with $(1+x{)}^{30}(1+x)$ gives $\left(\genfrac{}{}{0ex}{}{30}{15}\right)\equiv -1(\mathrm{mod}31)$. Thus the plus-one, not minus-one, is divisible by 31.