Some of my elementary original problems
© Copyright: Cristinel Mortici

E11. Find prime numbers  such that

E10. Let  be integer. Prove that among the elements of the set

one can find the fourth power of an integer.

E9. The difference of two positive integers is equal to  Find them, knowing that the first number is a power of six and the second one is prime.

E8. Let  be integers, any two different, such that  Prove that

E7. Find all strictly increasing functions  such that  divides , whenever

E6. Prove that the number  can be written as the sum of two non-zero perfect squares in at least four ways.

E5. Let  be real numbers such that  and  Prove that

E4. Let  be prime numbers such that

Prove that

E3. Find all prime numbers  such that

E2. Let  be real numbers such that

Prove that

E1. The length sides  of a triangle  are positive integers such that

Prove that triangle  is isosceles, whose perimeter is equal to 2013.