MathDB

2

Part of 2011 Cuba MO

Problems(2)

1x2x2 in 20x20x20

Source: 2011 Cuba MO 1.2

9/18/2024
A cube of dimensions 20×20×2020 \times 20 \times 20 is constructed with blocks of 1×2×21 \times 2 \times 2. Prove that there is a line that passes through the cube but not any block.
geometry3D geometrycombinatoricscombinatorial geometry
3x^4-2024y+1= 0 diophantine

Source: 2011 Cuba MO 2.2

9/17/2024
Determine all the integer solutions of the equation 3x4−2024y+1=03x^4-2024y+1= 0.
diophantineDiophantine equationnumber theory