MathDB
P23 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014
modular arithmeticnumber theoryprime numbers

Problem Statement

Which of the followings is false for the sequence 9,99,999,9,99,999,\dots?
<spanclass=latexbold>(A)</span><span class='latex-bold'>(A)</span> The primes which do not divide any term of the sequence are finite.
<spanclass=latexbold>(B)</span><span class='latex-bold'>(B)</span> Infinitely many primes divide infinitely many terms of the sequence.
<spanclass=latexbold>(C)</span><span class='latex-bold'>(C)</span> For every positive integer nn, there is a term which is divisible by at least nn distinct prime numbers.
<spanclass=latexbold>(D)</span><span class='latex-bold'>(D)</span> There is an inteter nn such that every prime number greater than nn divides infinitely many terms of the sequence.
<spanclass=latexbold>(E)</span><span class='latex-bold'>(E)</span> None of above