Question

Prove that , [x] + [5 x] + [10 x] + [20 x] = 36 k + 35 , k ∈ I does not have any real solution. Here [.] denotes greatest integer function.

Answer 1

[x] + [5x] + [10x] + [20 x] = 36k + 35 ; k ∈ I

Let x = I + f