Orthogonal matrices with rational components in composing tests for High   School students
  Fermat Last Theorem, which inspired mathematicians during 300 years, is proved by Andrew Wiles. Even among mathematicians there is a narrow circle of specialists, who can read this proof and understand all details. Is it a reason for pessimism? No, since arithmetics if entire numbers contains broad variety of problems with a simple statement, which might be not less intricate. One of them arises in elementary geometry. 
Ruslan A. Sharipov