Understand the problem For a polynomial with integer coefficients and degree no less than , prove that there are infinitely many primes which satisfies the following. There exists an integer such that and is a multiple of . Source of the problem Korea Junior MO...

Understand the problem Determine the minimal and maximal values the expression can take, where are real numbers. Source of the problem Israel MO 2018, Problem 3 Topic Algebra, Inequality Difficulty Level 6/10 Suggested Book Excursion in Mathematics by Bhaskarcharya...

Understand the problem Find all positive rational that satisfy the equation : Source of the problem Greece MO 2019, Problem 3 Topic Number Theory Difficulty Level 7/10 Suggested Book Challenges and Thrills of Pre College Mathematics Start with hints Hint 0Hint 1Hint...

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...