VMO 1989 Problem 4

Do there exist integers m, n not both divisible by 5 such that $m^2$ + $19n^2$ = 198· $10^{1989}$ ?

Community text Kalva (prase.cz mirror). Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.