Let $N = 2010!+1$. Prove that a) $N$ is not divisible by $4021$; b) $N$ is not divisible by $2027,2029,2039$; c)$ N$ has a prime divisor greater than $2050$.
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Tags: number theory
Let $N = 2010!+1$. Prove that a) $N$ is not divisible by $4021$; b) $N$ is not divisible by $2027,2029,2039$; c)$ N$ has a prime divisor greater than $2050$.