Customers of a phone company can choose between two service plans for long distance calls. the first plan has no monthly fee but charges $0.18 for each minute of calls. the second plan has an $18 monthly fee and charges an additional $0.14 for each minute of calls. for how many minutes of calls will the costs of the two plans be equal?

The solution would be like this for this specific problem:

Let x be equal to the number of minutes per month and y be equal to the total cost. Utilizing these variables, we can write an equation that can represent each calling plan. 

Plan 1: y = (.18)x 
Plan 2: y = (.14)x + 18 

Now, we can solve for x (minutes of calls per month) by integrating the two equations. There are a lot of ways we can do this, but we can use the one below: 

y = (.18)x = (.14)x + 18

(.18)x - (.14)x = 18

(.04)x = 18

x = 450 minutes

Therefore, the cost of the two plans will be equal when each of the plan use 450 minutes of call per month.

(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