MathDB

2

Part of 2023 Girls in Mathematics Tournament

Problems(2)

One of a, b, c is zero?

Source: 2023 Girls in Mathematics Tournament- Level A, Problem 2/ Level B, Problem 1

10/29/2023
Let a,b,ca,b,c real numbers such that an+bn=cna^n+b^n= c^n for three positive integers consecutive of nn. Prove that abc=0abc= 0
algebra
Quadruples (a,b,x,y) such that n= ax+by, and a>b

Source: 2023 Girls in Mathematics Tournament- Level B, Problem 2

10/29/2023
Given nn a positive integer, define TnT_n the number of quadruples of positive integers (a,b,x,y)(a,b,x,y) such that a>ba>b and n=ax+byn= ax+by. Prove that T2023T_{2023} is odd.
algebranumber theory