Evaluate the sum of reciprocals of double factorial of even nonnegative integers.
x^3 + y^3 + z^3 = w^3
The smallest set of positive integers x,y,z,w qualifying as a solution of the bolded equation above is:
a.Find some other sets of distinct integers, not necessarily positive.
b. Provide some comments on "The sum of 3 cubes is a cube" equation.
One Martian, one Venusian and one Human reside on Pluto.
One day they make the following conversation:
Martian: I have spent 1/12 of my life in Pluto.
Human: I also have.
Venusian: Me too.
Martian: But Venusian and I have spent much more time here than you, Human.
Human: However Venusian and I are of the same age.
Venusian: I have lived 300 Earth years.
Martian: Venusian and I have been on Pluto for the last 13 years.
It is known that Human and Martian together have lived for 104 Earth years.
Find their respective ages.
The numbers are not necessarily expressed in base 10 .
Source: 1971 IMO longlisted problem.
How many ones are used in writing all of the numbers from 0 to 2018 (inclusive) in binary form?