MathDB

4

Part of 2023 Puerto Rico Team Selection Test

Problems(2)

n = a^2 + b^2 + c^2 + d^2 - Puerto Rico TST 2023.1.4

Source:

3/23/2024
Find all positive integers nn such that: n=a2+b2+c2+d2,n = a^2 + b^2 + c^2 + d^2, where a<b<c<da < b < c < d are the smallest divisors of nn.
number theory
3 jumps of a frog on lattice points

Source: Puerto Rico TST 2023.2.4

3/24/2024
A frog started from the origin of the coordinate plane and made 33 jumps. Each time, the frog jumped a distance of 55 units and landed on a point with integer coordinates. How many different position possibilities end of the frog there?
combinatorics