Number Theory, Korea Junior MO 2015, Problem 7

Number Theory, Korea Junior MO 2015, Problem 7

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...
Inequality, Israel MO 2018, Problem 3

Inequality, Israel MO 2018, Problem 3

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...
Number Theory, Greece MO 2019, Problem 3

Number Theory, Greece MO 2019, Problem 3

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...
Algebra, Germany MO 2019, Problem 6

Algebra, Germany MO 2019, Problem 6

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...
Geometry, Israel MO 2019, Problem 3

Geometry, Israel MO 2019, Problem 3

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...
Combinatorics, Israel MO 2014, Problem 4

Combinatorics, Israel MO 2014, Problem 4

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...