2022 Polish Junior Math Olympiad: Unraveling Prime Number Patterns

Get ready to dive into the fascinating world of prime numbers with a challenging problem from the 2022 Polish Junior Math Olympiad. In this video, we'll explore the question of finding positive integer(s) 𝒏 for which both numbers 𝟏 ⏟(𝟕𝟕…𝟕)┬(𝒏 𝐬𝐞𝐯𝐞𝐧𝐬) and (𝟑⏟(𝟕𝟕…𝟕))┬(𝒏 𝐬𝐞𝐯𝐞𝐧𝐬) are prime numbers.

While it's evident that n=1 is a possible solution, we need to prove that it is the only solution. We'll unravel the patterns and logic behind prime numbers and employ various mathematical techniques to tackle this problem step by step.

Join us on this educational journey as we explore the intricacies of prime numbers, delve into the Polish Junior Math Olympiad problem, and work together to unravel the mystery of the only solution. With a resilient and determined mindset, you'll enhance your problem-solving skills and have fun along the way. Are you up for the challenge? Let's go!