MathDB

3:

Part of 1994 Romania TST for IMO

Problems(3)

romania tst

Source: Romania TST for IMO 1994 second exam

9/6/2017
Let a1,a2,...,ana_1, a_2, . . ., a_n be a finite sequence of 00 and 11. Under any two consecutive terms of this sequence 00 is written if the digits are equal and 11 is written otherwise. This way a new sequence of length n−1n -1 is obtained. By repeating this procedure n−1n - 1 times one obtains a triangular table of 00 and 11. Find the maximum possible number of ones that can appear on this table
combinatoricsalgebra
easy old exercice

Source: Romania TST for IMO 1994

9/6/2017
Prove that the sequence an=3n−2na_n = 3^n- 2^n contains no three numbers in geometric progression.
number theory
easy problem

Source: Romania TST for IMO 1994,third test

9/6/2017
Determine all integer solutions of the equation xn+yn=1994x^n+y^n=1994 where n≥2n\geq 2
number theory