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The Fifteenth Canadian Mathematical Olympiads
1983年第十五届加拿大数学奥林匹克
  1. Find all solutions to n! = a! + b! + c! .
  2. Find all real-valued functions f on the reals whose graphs remain unchanged under all transformations (x, y) → (2kx, 2k(kx + y) ), where k is real .
  3. Is the volume of a tetrahedron determined by the areas of its faces ?
  4. Show that we can find infinitely many positive integers n such that 2n - n is a multiple of any given prime p .
  5. Show that the geometric mean of a set S of positive numbers equals the geometric mean of the geometric means of all non-empty subsets of S .
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