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About the divisors of 1111...11(2011 ones)

Source: Albanian BMO TST 2010 Question 1

March 20, 2010
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

a) Is the number 1111⋯11 1111\cdots11 (with 2010 2010 ones) a prime number? b) Prove that every prime factor of 1111⋯11 1111\cdots11 (with 2011 2011 ones) is of the form 4022j\plus{}1 where j j is a natural number.
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