MathDB

3

Part of 2014 Czech-Polish-Slovak Junior Match

Problems(2)

3x2 tiles in a 7x7 boards

Source: Czech-Polish-Slovak Junior Match 2014, Individual p3 CPSJ

3/13/2020
We have 1010 identical tiles as shown. The tiles can be rotated, but not flipper over. A 7×77 \times 7 board should be covered with these tiles so that exactly one unit square is covered by two tiles and all other fields by one tile. Designate all unit sqaures that can be covered with two tiles. https://cdn.artofproblemsolving.com/attachments/d/5/6602a5c9e99126bd656f997dee3657348d98b5.png
tilesTilingcombinatorics
|n^3 - 4n^2 + 3n - 35| and |n^2 + 4n + 8| are primes

Source: Czech-Polish-Slovak Junior Match 2014, Team p3 CPSJ

3/23/2020
Find with all integers nn when ∣n3−4n2+3n−35∣|n^3 - 4n^2 + 3n - 35| and ∣n2+4n+8∣|n^2 + 4n + 8| are prime numbers.
number theoryprimesprime