MathDB

1

Part of 2024 India Regional Mathematical Olympiad

Problems(2)

RMO 2024 Q1

Source: RMO 2024 Q1

11/3/2024
Let n>1n>1 be a positive integer. Call a rearrangement a1,a2,⋯ ,ana_1,a_2, \cdots , a_n of 1,2,⋯ ,n1,2, \cdots , n nice if for every k=2,3,⋯ ,nk = 2,3, \cdots , n, we have that a1+a2+⋯+aka_1 + a_2 + \cdots + a_k is not divisible by kk. (a) If n>1n>1 is odd, prove that there is no nice arrangement of 1,2,⋯ ,n1,2, \cdots , n. (b) If nn is even, find a nice arrangement of 1,2,⋯ ,n1,2, \cdots , n.
number theory
RMO KV 2024 Q1

Source: RMO KV 2024 Q1

11/3/2024
Find all positive integers x,yx,y such that 202x+4x2=y2202x + 4x^2 = y^2.
number theory