MathDB

sum of digits in decimal represent. of 4x^4+y^4-z^2+4xyz at most 2

Source: Mediterranean Mathematical Olympiad 2019 P3 MMC

July 21, 2019

number theorydecimal representationsum of digits

Problem Statement

Prove that there exist infinitely many positive integers

x,y,z

for which the sum of the digits in the decimal representation of

~4x^4+y^4-z^2+4xyz

~

is at most

2

.
(Proposed by Gerhard Woeginger, Austria)