To prove: n 3 − n is divisible by 3 for all natural number n .

Question

Want to see the full answer?

Answer 1

Question

Chapter C, Problem 12E

To determine

To prove:

$n^{3} - n$ is divisible by $3$ for all natural number n.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

The number of fish swimming upstream to spawn is approximated by the function given below, where x represents the temperature of the water in degrees Celsius. Find the water temperature that produces the maximum number of fish swimming upstream. F(x) = x3 + 3x² + 360x + 5017, 5≤x≤18

A campground owner has 500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let x represent the width of the field. (a) Write an expression for the length of the field as a function of x. (b) Find the area of the field (area = length x width) as a function of x. (c) Find the value of x leading to the maximum area. (d) Find the maximum area. x River

A rectangular tank with a square base, an open top, and a volume of 1372 ft³ is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The dimensions of the tank with minimum surface area are (Simplify your answer. Use a comma to separate answers.) ft.