🌟 [ 27 ]   Can you solve this tricky number theory problem? Serbia TST 2014 [ @Shefs of Problem Solving ]

Latex: We call natural number $n$ $crazy$ iff there exist natural numbers $a$, $b \ge 2$ such that $n=a^b+b$. Whether there exist $2014$ consecutive natural numbers among which are $2012$ $crazy$ numbers? Timestamps: 00:00 Intro 45 - 60/120 - 240 Take 20 00:52 Problem Solving Philosophy and Thinking 02:05 Can we construct 2 funny numbers? 03:30 Take 10-20-30 minutes 03:50 An idea 05:00 Can we make 3 funny numbers? 06:00 Generalizing the idea 08:00 What we have and what we need 10:55 Another major problem about the problem 11:40 The finishing idea 14:10 Prime shifting trick for the finish! 15:50 Thanks for problem solving

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