Factorial problem by Ashu Dablo

Number Theory Level 3

Find the largest positive integer n, such that \(n!\) can be expressed as the product of \((n-2^{11})\) consecutive integers.

Let a positive integer \(x\) be \(\equiv n \pmod{71\times 73\times 79}\)

Find \(x\) \(\pmod{41\times 47}\)

x is the remainder when n is divided by 409457 (409457=71x73x79).

The answer is the remainder when x is divided by 1927. (1927=41*47)

This problem is inspired from Interesting property of 7! by Agnishom Chattopadhyay.

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