Question 2
a) Find the smallest positive integer $n$ such that $(n+1)(n+2)(n+3)(n+4)$ is divisible by $1000$.
b) Prove that there are no positive integers $a,b$ for which $a^4+324b^4$ is prime.
b) Prove that there are no positive integers $a,b$ for which $a^4+324b^4$ is prime.