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in Olympiad by (65.8k points)

For each positive integer n, consider the highest common factor hn of the two numbers n! + 1 and (n + 1)!. For n < 100, find the largest value of hn.

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HCF of ((n! + 1), (n + 1)!) = h , n < 100

If n + 1 is prime then n! + 1 is divisible by (n + 1).

Also (n + 1)! is divisible by it.

∴ For n + 1 = 97

HCF of 96! + 1 & 97! = 97

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