MathDB

Problem 1

Part of 1994 French Mathematical Olympiad

Problems(1)

# of n for which 50^n<7^p<50^(p+1) forms a sequence

Source: France 1994 P1

5/7/2021
For each positive integer nn, let InI_n denote the number of integers pp for which 50n<7p<50n+150^n<7^p<50^{n+1}.
(a) Prove that, for each nn, InI_n is either 22 or 33. (b) Prove that In=3I_n=3 for infinitely many n∈Nn\in\mathbb N, and find at least one such nn.
Sequencealgebra