Can the sum of three different natural numbers be divisible by each summand?

📜 Leaflet #divisibility

✍ Write your answer in the comments!

Find all prime numbers for which the square of this number increased by 4 and the square of this number increased by 6 are also prime numbers.

📜 Leaflet #Prime_number

🌐 Wikipedia

✍️ Write your answer in the comments!

Find all prime numbers p for which p = a + b = c - d, where a, b, c, d are prime numbers (not necessarily distinct).

📜 Leaflet #Prime_number

✍️ Write your answer in the comments!

Olivia drew a polygon and Liam cut it into a triangle and a quadrilateral. How many sides could Olivia's polygon have? Find all the variants and prove that there are no others.

📜 Leaflet #geometry

✍️ Write your answer in the comments!