3

Part of 2019 Mediterranean Mathematics Olympiad

Problems(1)

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

Source: Mediterranean Mathematical Olympiad 2019 P3 MMC

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

~

2

.
(Proposed by Gerhard Woeginger, Austria)

number theorydecimal representationsum of digits