http://destiny.wikia.com/wiki/Crux_of_Crota
You need to have the eidolon equipped while killing crota?
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Does anybody know if it somehow matters if you have done normal mode before? We've done a lot of hard runs and one member of our fire team has received the crux the third time now, while all others did not even get one. Usually we are doing normal mode before hard and this guy doesn't attend the normal runs.