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Recall the notation $(z;q)_n=(1-z)(1-zq)(1-zq^2)\cdots(1-zq^{n-1})$. My earlier MO question did not find enough interest or yield an answer. Perhaps the modulo $2$ part might have thrown people off. ...

This quest arose from certain calculations with integer partitions (having distinct parts) and the corresponding values of their Dyson ranks. I would like to ask: QUESTION. Is this congruence true ...