MathDB

1

Part of 1996 IberoAmerican

Problems(2)

11st ibmo - costa rica 1996/q1.

Source: Spanish Communities

4/23/2006
Let n n be a natural number. A cube of edge n n may be divided in 1996 cubes whose edges length are also natural numbers. Find the minimum possible value for n n.
geometry3D geometrynumber theory unsolvednumber theory
11st ibmo - costa rica 1996/q4.

Source: Spanish Communities

4/23/2006
Given a natural number n≥2n \geq 2, consider all the fractions of the form 1ab\frac{1}{ab}, where aa and bb are natural numbers, relative primes and such that: a<b≤na < b \leq n, a+b>na+b>n. Show that for each nn, the sum of all this fractions are 12\frac12.
inductionnumber theory unsolvednumber theory