MathDB

4

Part of 2024 Girls in Mathematics Tournament

Problems(2)

a^3+b^3+c^3= 2p and 3ab=2c^2

Source: 2024 Girls in Mathematics Tournament, Level A, Problem 4

10/26/2024
Find all the positive integers a,b,ca,b,c such that 3ab=2c23ab= 2c^2 and a3+b3+c3a^3+b^3+c^3 is the double of a prime number.
algebranumber theory
find all a such that n\mid phi(n)!+a for infinitely many n

Source: 2024 Girls in Mathematics Tournament- Level B, Problem 4

10/26/2024
Find all integers aa such that there are infinitely many positive integers nn such that nn divides ϕ(n)!+a\phi(n)!+a.
number theoryphi function