For every positive even integer n, the function h(n) is defined to be
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09 Jul 2021, 04:31
I just figured out a simple way to think of this question:
Let's not look at a big number like 2^50*50!+1.
Take 4!+1 as an example: 1x2x3x4=24 and 4!+1=25
4! has the biggest prime factor 3, while 4!+1 has the smallest and the only prime factor 5.
We can see that 4!+1 has the smallest prime factor that is bigger than the biggest prime factor in 4!.
Not so sure if it works for bigger numbers?
Take 5!+1 as another example: 1x2x3x4x5=120 and 5!+1=121.
5! has the biggest prime factor 5, while 5!+1 has the smallest and the only prime factor 11.
From the analogy, we can see that whatever x! is, the smallest prime factor of x!+1 will be bigger than x.
Now, we have 50! (let's ignore 2^50, for it does not affect the calculation) here, and the question asks for the smallest prime factor of 50!+1. From the analogy above, we are able to suggest that the smallest prime factor of 50!+1 would be bigger than 50. Thus, E (greater than 40) would be the answer.