Final stage of Israeli students competition, 2010. Duration: 4.5 hours
... 1. Prove that there exists an integer n, such that n2 + 3 is divisible by 75770. Solution. There’s nothing so special about this year, so we shall prove that for every natural m, we can find n such that n2 + 3 is divisible by 7m. The base of induction is simple: 22 + 3 is divisible by 7. The step of ...
... 1. Prove that there exists an integer n, such that n2 + 3 is divisible by 75770. Solution. There’s nothing so special about this year, so we shall prove that for every natural m, we can find n such that n2 + 3 is divisible by 7m. The base of induction is simple: 22 + 3 is divisible by 7. The step of ...
