1.Let a , b , c be the lenghts of the edges of a right parallelepiped and d be the the lenght og its diagonal .Prove that .

2.Prove that for 1 , k = 1………….n the inequality

3.Prove that for every integer n 2 , the number is not a prime .

4.Show that there exist infinetely many such that for any the number is not an prime .

5.Prove that for any integer n 1 , the number can be written as the product of four distinct integers .

6. : Prove that the function ,

where f(x) = ………+ –.

One can easily check that f(x) = 0 for x .

prove that is a periodic function with period

.

7.If a function is not an one -to -one function and there exist a function such that for all x,y .Show that f is a periodic function .

8.Let is a function such that the set {} has infinetely many elements .Prove that the period off is irrational .