MathDB

4

Part of 2020 Francophone Mathematical Olympiad

Problems(2)

2^x + 9 \cdot 7^y = z^3 for integers x,y,z>=0

Source: The Francophone MO Juniors P4

8/10/2020
Find all the integers x,yx, y and zz greater than or equal to 00 such that 2x+9⋅7y=z32^x + 9 \cdot 7^y = z^3
number theoryDiophantine equationdiophantineFrancophone
Prove that the set for which the number of prime divisors is bounded is finite

Source: The francophone mathematical olympiads P4

6/27/2020
Let (ai)i∈N(a_i)_{i\in \mathbb{N}} a sequence of positive integers, such that for any finite, non-empty subset SS of N\mathbb{N}, the integerΠk∈Sak−1\Pi_{k\in S} a_k -1is prime. Prove that the number of aia_i's with i∈Ni\in \mathbb{N} such that aia_i has less than mm distincts prime factors is finite.
number theoryFrancophone