Number Theory, Ireland MO 2018, Problem 9

Number Theory, Ireland MO 2018, Problem 9

Understand the problem The sequence of positive integers satisfies for .Prove that there exists at most one for which is the cube of an integer. Source of the problem Ireland MO 2018, Problem 9 Topic Number Theory Difficulty Level 8/10 Suggested Book Excursion in...
Number Theory, France IMO TST 2012, Problem 3

Number Theory, France IMO TST 2012, Problem 3

Understand the problem Let be a prime number. Find all positive integers such that: Source of the problem France IMO TST 2012, Problem 3 Topic Number Theory Difficulty Level 7/10   Suggested Book Challenges and Thrills of Pre College Mathematics Start with...
Algebra, Austria MO 2016, Problem 4

Algebra, Austria MO 2016, Problem 4

Understand the problem Let be real numbers with .Prove that , and determine the cases of equality. Source of the problem Austria MO 2016. Final Round, Problem 4 Topic Inequality Difficulty Level Suggested Book Challenges and Thrills of Pre-College Mathematics Start...
Number Theory, Cyprus IMO TST 2018, Problem 1

Number Theory, Cyprus IMO TST 2018, Problem 1

Understand the problem Determine all integers for which the number in base is a perfect square. Source of the problem Cyprus IMO TST 2018, Problem 1 Topic Number Theory Difficulty Level 7/10 Suggested Book Challenges and Thrills of Pre College Mathematics Start...
Number Theory, South Africa 2019, Problem 6

Number Theory, South Africa 2019, Problem 6

Understand the problem Determine all pairs of non-negative integers that satisfy the equation Source of the problem South Africa MO 2019, Problem 6 Topic Number Theory Difficulty Level 7/10 Suggested Book Excursion in Mathematics by Bhaskaracharya Prathisthan Start...