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1

Part of 2013 Romanian Master of Mathematics

Problems(1)

RMM 2013 Problem 1

Source:

3/2/2013
For a positive integer aa, define a sequence of integers x1,x2,…x_1,x_2,\ldots by letting x1=ax_1=a and xn+1=2xn+1x_{n+1}=2x_n+1 for n≥1n\geq 1. Let yn=2xn−1y_n=2^{x_n}-1. Determine the largest possible kk such that, for some positive integer aa, the numbers y1,…,yky_1,\ldots,y_k are all prime.
floor functionmodular arithmeticquadraticsnumber theory