MathDB
Nice Number Theory

Source: Azerbaijan JBMO TST Day1 P3

May 31, 2017
number theory

Problem Statement

Let a,b,c,d,ea, b, c, d, e be positive and different divisors of nn where nāˆˆZ+n \in Z^{+}. If n=a4+b4+c4+d4+e4n=a^4+b^4+c^4+d^4+e^4 let's call nn "marvelous" number.
a)a) Prove that all "marvelous" numbers are divisible by 55.
b)b) Can count of "marvelous" numbers be infinity?
Back to ProblemsView on AoPS