Talmud for Numbers 31:19

What is the reason of the House of Shammai? You and your captives¹⁴⁴Num. 31:19, speaking of the captive Midianite women.. Since you could not be impure before you entered the covenant, also your captives cannot be impure before they enter the covenant¹⁴⁵While it seems from the text there that a Gentile corpse imparts impurity of the dead by touch, it is clear that a living Gentile cannot biblically be impure; the impurities attributed to Gentiles are of purely rabbinic character and must be disregarded in matters of conversions. Sifry Num. # 157 notes that mention of the captives in relation to impurity implies that these had to be converted.. What is the reason of the House of Hillel? You and your captives. Since you need sprinkling on the third and seventh {days}, so your captives need sprinkling on the third and seventh {days}. But it is not logically consistent¹⁴⁶There is no claim that the restrictive practice of the House of Hillel is biblical., since Rav Ḥiyya bar Joseph, Giddul bar Benjamin said in the name of Rav: The House of Hillel agree that if he transgressed and poured the blood, that it is accepted.