1. both A and B are divisible by N

2. both A and B are NOT divisible by N

You can never expect A+B to be divisible by N when only A or B alone is divisible by N.

How can this knowledge be applied to the problem?

Well … you may want to take A = h(100) and B = 1. As you can see, B cannot be divisible by numbers other than 1, while A is at least divisible by integers from 1 to 50. In other words, the integers that won’t divide A are greater than 50. Therefore, the smallest prime factor of or the smallest integer that divides h(100) + 1 must be greater than 50.

]]>1. both A and B are divisible by N

2. both A and B are NOT divisible by N

You can never expect A+B to be divisible by N when only A or B alone is divisible by N.

How can this knowledge be applied to the problem?

Well … you may want to take A = h(100) and B = 1. As you can see, B cannot be divisible by numbers other than 1, while A is at least divisible by integers from 1 to 50. In other words, the integers that won’t divide A are greater than 50. Therefore, the smallest prime factor of or the smallest integer that divides h(100) + 1 must be greater than 50.

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