The central problem in additive number theory is to determine if a given set of integers is a basis of finite order.
Take for example the square numbers. According to Lagrange's theorem every integer can be represented as a sum of at most four squares. ( The number 7 for example, requires four squares: 7 = 2^2 + 1^2 + 1^2 + 1^2. ) In this example the set of squares is a basis of order 4.
Goldbach's conjecture is a famous problem in additive number theory.
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
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