2018/016) For what natural numbers can the product of some numbers of $n,n+1,n+2,n+3,n+4,n+5$ be same as product of other numbers

As it is sequence of 6 consecutive numbers more than one number cannot be divisible by 7.

If one number is divisible by 7 then it cannot be divided to 2 groups for product to be same.

So the numbers have to be  of the form 7m+1,7m+2,7m+3,7m+4,7m+5,7m+6 and product of them mod 7 is 6. and hence it is not a square ( square mod 7 are 1,4,2).

So no solution exists