What is the meaning of "Vayachalosh Yehoshua ... "?
1.
Rashi: It means that Yehoshua severed the heads of Amalek's strong men, keeping alive only the weak ones. He did not kill them all, due to the Divine command.
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2.
Rashbam: It means that he completely vanquished Amalek.
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Lev Eliyahu (p.97): This is because Hashem makes a nation fall only after its angel has fallen, and the angel of Eisav will not fall as long as the Yetzer ha'Ra is among us.