"Styczeń ma trzydzieści jeden dni."

Translation: January has thirty-one days.

[eannaoc]

Is "dni" here in accusative or genetive? Does the 'jeden' alter the case here (?accus) or the trzydzieści (?gen)?

[Jellei]

Very good question. It's Genitive, though.

Compare "trzydzieści jeden kobiet" (Genitive) and "trzydzieści dwie/trzy/cztery kobiety" (Accusative) to see it more easily.

[ankbhatnagar]

But you said elsewhere that numbers ending with _1, _2, _3 and _4, except 11, 12, 13 and 14 take nominative/accusative. So days (dni) should be accusative here, shouldn't be?

[alik1989]

You probably meant this comment:

https://forum.duolingo.com/comment/26135406?comment_id=26139289

He wrote:

1, 2, 3, 4 and numbers ending with -2, -3, -4 BUT NOT -12, -13, -14 take Nominative.

So, it's correct, albeit a bit oversimplified, because it doesn't take other cases into account. Here's the full pattern:

https://forum.duolingo.com/comment/18126859?comment_id=48113545