Understand the problem Suppose that real numbers and satisfy the following equations: Show that must be equal to or . Note: It is not required to show the existence of such numbers . Source of the problem Germany MO 2019, Problem 6 Topic Algebra, Simultaneous...
Understand the problem Six congruent isosceles triangles have been put together as described in the picture below. Prove that points M, F, C lie on one line. Source of the problem Israel MO 2019 Problem 3 Topic Geometry Difficulty Level 6/10 Suggested Book Challenges...
Understand the problem The three-digit number 999 has a special property: It is divisible by 27, and its digit sum is also divisible by 27. The four-digit number 5778 also has this property, as it is divisible by 27 and its digit sum is also divisible by 27. How many...
Understand the problem Show that for each non-negative integer there are unique non-negative integers and such that we have Source of the problem Germany MO, 2019, Problem 4 Topic Number Theory Difficulty Level 4/10 Suggested Book Challenges and Thrills of Pre...
Understand the problem Given the polynomial where is a positive integer. Prove that can’t be written as a product of non-constant polynomials with integer coefficients. Source of the problem Vietnam MO 2014 Problem 2 Topic Polynomial, Algebra Difficulty...
Understand the problem Let be prime numbers Prove that if is a perfect square then is not a perfect square for any positive integer Source of the problem Italy MO 2019, Problem 2 Topic Number Theory Difficulty Level 5/10 Suggested Book Challenges and Thrills of...
