This problem was asked in IMO 1970, Hungary.

Q: For what natural numbers n can the product of some of the numbers n,n+1,n+2,n+3,n+4,n+5 be equal to the product of the remaining ones?

Note that since there are 6 numbers under consideration, if a prime number p divides any of these numbers, it cannot be greater than 5.

In the set of numbers n+1,n+2,n+3,n+4, there can be no common prime divisor greater than 2 or 3. Also, since two of these four numbers must be odd, they must be powers of 3. But this isn’t possible since no two powers of 3 differ by 2.

Therefore, there is no such n

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