5

Part of 2019 New Zealand MO

Problems(2)

n^4 - n^3 + 3n^2 + 5 is a perfect square

Source: New Zealand MO 2019 Round 1 p5

Find all positive integers

n

n^4 - n^3 + 3n^2 + 5

is a perfect square.

number theoryPerfect Square

equilateral triangle is partitioned into smaller equilateral triangular pieces

Source: 2019 New Zealand MO Round 2 p5 NZMO

An equilateral triangle is partitioned into smaller equilateral triangular pieces. Prove that two of the pieces are the same size.

combinatorial geometrygeometrycombinatoricsEquilateralequilaterals