What Are Some Accessible Unsolved Problems in Number Theory for Teens?

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The Goldbach Conjecture is highlighted as an accessible unsolved problem in number theory for teens, stating that every even number greater than 2 can be expressed as the sum of two prime numbers. The discussion emphasizes that while these problems are straightforward to articulate, they remain challenging to prove. The book "Unsolved Problems in Number Theory" by R.K. Gay is recommended as a resource that contains many such problems that are easy to grasp. Engaging with these unsolved problems can inspire young mathematicians. Exploring these topics can foster a deeper interest in number theory among teens.
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What are the most interesting examples of unsolved problems in number theory which an 18 year can understand?
 
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The Goldbach Conjecture is easy enough to understand: every even number greater than 2 is the sum of two prime numbers.
Easy to state, fiendishly difficult to prove.
 
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A lot are referenced in the book :
"Unsolved problems in number theory", R.K.Gay, Springer Edit.
Much of them are easy to understand.
 
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