Alex buys a car with a down payment along with a monthly payment. if he pays $5,250 for the down payment, pays the monthly payment for 14 months, and the total cost of the car is $13,650, how much money does alex pay per month for the monthly payment?

(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

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