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Primes in a seqeunce

Source: Finnish Mathematics Competition 1999, Final Round, Problem 3

November 14, 2011
modular arithmeticgeometric seriesalgebradifference of squaresspecial factorizationsnumber theory unsolvednumber theory

Problem Statement

Determine how many primes are there in the sequence 101,10101,1010101....101, 10101, 1010101 ....