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Part of 2010 Silk Road

Problems(1)

SRMC 2010 P2

Source:

12/7/2015
Let N=2010!+1N = 2010!+1. Prove that a) NN is not divisible by 40214021; b) NN is not divisible by 2027,2029,20392027,2029,2039; c)N N has a prime divisor greater than 20502050.
number theory