ärztlichem
ärztlichem is a form of the German adjective ärztlich, meaning medical or physician-related. It is the dative singular form used before masculine or neuter nouns when the noun is not preceded by an article (strong declension). For example: mit ärztlichem Rat (with medical advice) and auf ärztlichem Weg (in a medical way, along a medical path).
When a definite article is used, the ending changes to -en, as in dem ärztlichen Rat or
The base adjective is derived from Arzt (doctor) plus the suffix -lich, yielding meanings related to medicine,
In summary, ärztlichem is the dative singular form of ärztlich used with masculine or neuter nouns without