Luke's motel rents rooms with 2 beds for $65 and rooms with 1 bed for $56. on a given night luke's motel takes in $4836, and twice as many double how many single-bed rooms were rented?

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18