13305

13305 is a number that appears in various contexts, including mathematics, astronomy, and popular culture. In mathematics, 13305 is known for being the smallest number that can be expressed as the sum of two positive cubes in two different ways: 13305 = 10^3 + 15^3 = 1^3 + 110^3. This property makes it a part of the study of Diophantine equations, which are polynomial equations with integer coefficients.

In astronomy, 13305 is the number assigned to the asteroid (13305) 1998 RO1, discovered in 1998. This asteroid is part of the main asteroid belt between Mars and Jupiter. It has an estimated diameter of about 10 kilometers and orbits the Sun with a period of approximately 4.4 years.

In popular culture, 13305 is referenced in the television series "The Big Bang Theory," where it is mentioned as a number that Sheldon Cooper, one of the main characters, finds interesting due to its mathematical properties. The number also appears in the video game "Portal 2," where it is part of a series of numbers that the player must input to solve a puzzle.

Overall, 13305 is a number with diverse appearances and significance across different fields, from mathematics to astronomy and popular culture.