Is This Algebra or Number Theory? (Part 2)

Number Theory Level 4

Find the largest possible value of positive integer n n , such that n ! n! can be expressed as the product of ( n − 4 ) (n-4) consecutive positive integers.


Notation: ! ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .

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The answer is 119.

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Fidel Simanjuntak by Fidel Simanjuntak , 19, Indonesia

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1 solution

Sajjan Barnwal
May 9, 2017

We need four less numbers that means (n+1) will be multiplied to the product of those (n-4) numbers to keep n! to the same value. If we remove 1,2,3,4,5 that is product of those is 120 ..so n=119.

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