Translation:Двадцять один студент
Ukrainian treats nouns after plurals differently from English. In English, you use a plural form after any number more than 1. So, twenty-one is considered more than 1, so you use a plural noun.
In Ukrainian, you break down the number into words and look at the last word. So, два́дцять оди́н ends in оди́н, so you use a plural nominative noun.
If that helps, you can consider this an omited 'and': «два́дцять [студе́нтів і] один студе́нт» "twenty [students and] one student". Like "thousand nights and one night".
By the way, the exact rules for choosing the correct form are a bit complicated than in English. Three forms are used:
- After «один», you use nominative singular (студе́нт).
- After «два» '2', «три» '3', «чоти́ри» '4', you use nominative plural: два студе́нти 'two students'.
- After all the other number words, you use genitive plural: п’ять студе́нтів 'five students'.
Is it nominative plural for 2, 3 and 4, or genitive singular? We have 2 ока, 2 плеча, 2 ноги, 2 голови - last two with the accent on the last syllable, like in genitive singular. This is the remnant of the doubles, which were once used in Proto-Slavic. I'm not sure if it's better to say 2 ножа, 2 стола or 2 ножі, 2 столи. But we will definitely say 2 коня, 2 кота, 2 слона, not 2 коні, 2 коти, 2 слони. So it's genitive singular, at least in most cases (I have an impression that it's starting to shift in the language just now in the cases like ножі and столи, but it's not the general rule still).
Is it nominative plural for 2, 3 and 4, or genitive singular?
Well... I don't really trust my judgements here. I'm using a lot of genitive singular forms, but I've always thought those are due to influence of Russian. So, I'm relying on the prescriptive rules.
Most descriptions of Ukrainian (e.g. this or this) say Nominative plural is the default form, and Genitive is an exception. (I didn't list those exceptions here lest I should make the matter more confusing than it's already is.)
According to the descriptions I've read, nominative plural is the default case, and genitive singular is used:
- for nouns that have the -ин- suffix in singular, but not in plural: п’ятдесят чотири селянина '54 villagers'; два імені 'two names';
- when the noun is placed before the numeral to express inexact number: років два, діб зо три, тижнів чотири,
- often with neuter nouns: два нових (нові) відра, три гірських (гірські) озера (not found in most descriptions, mentioned here),
- sometimes, when a nominative plural and gentivie singular have different stress, nominative plural is used after «два», «три», «чоти́ри», but with genitive singular's stress: n.pl. се́ла, g. sg. села́, so we use чоти́ри села́ (which apparently is same as genitive singular).
But we will definitely say 2 коня, 2 кота, 2 слона, not 2 коні, 2 коти, 2 слони. So it's genitive singular, at least in most cases (I have an impression that it's starting to shift in the language just now in the cases like ножі and столи, but it's not the general rule still).
The prescriptive rules certainly favour Nominative plural. Those rules might be out-of-touch with the real usage, however.
I can't comment on real-world usage, since I live outside of Ukraine, and it's difficult to google such things, since I keep getting Russian texts in the search results.
So it even more complicated than I thought :) I would hypothesize that a long time ago this all was genitive singular, and then started to change, but, as always in languages, changes don't come in a uniform way. So now we have a new rule with a good deal of old exceptions. I wonder what linguists would say...