Quantitative Finance
# Problem Solving Skills

Consider a statement $S(N): 1+3+5+\cdots+(2N-1)=7+N^2,$ then which of the following is true?

What is the remainder when ${105}^{165}-1$ is divided by 4?

If $\displaystyle a_n=2^{2^n}+1$ for $n > 1,$ then what is the last digit of $a_{451}?$