The first part of Mysticials answer is correct, idiv does a 128/64 bit division, so the value of rdx, which holds the upper 64 bit from the dividend must not contain a random value. But a zero extension is the wrong way to go.
As you have signed variables, you need to sign extend rax to rdx:rax. There is a specific instruction for this, cqto (convert quad to oct) in AT&T and cqo in Intel syntax. AFAIK newer versions of gas accept both names.
movq %rdx, %rbx cqto # sign extend rax to rdx:rax idivq %rbx
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