What is the grammatical difference between these two sentences:
- Die Lehrer essen nicht größere Eier.
- Die Lehrer essen keine größeren Eier.
Why the ending -n in the second sentence?
The difference is that the first sentence is wrong. You always negate sentences like that by using "keine/n".
The -n in the second sentence is there because it's accusative.
(You can use "nicht" in the first case by putting it at the end of the sentence: "Die Lehrer essen größere Eier nicht." But that's very archaic and stresses the negation. It should be used only in poems and other literary work.)
The first sentence seems also a bit wrong to me, and perhaps there must be also an addition by putting some kind of explaination to be correct, example:
Your (wrong) sentence:
So you will use this first sentence mostly in cases when you add an explaination or consequence.
Your second sentence:
It is correct, you say that mostly if they never do at all, maybe because they are always talking and their mouth always busy. Or "A snake don't eat an elephant."
1) Die Lehrer essen größere Eier nicht.
Both, größere and größeren, are plural accusative flexions of the comparative adjective größer. If you take a look at the flexion tables for größer, you'll see that größere is used in the plural accusative case when there is no article before the adjective (see under 'Ohne Artikel') – which applies to sentence 1). Größeren is used in the accusative case if it is preceded by an indefinite article (see under 'Unbestimmter Artikel'.)
The -en ending in sentence 2) is due to the declension pattern that applies to attributive adjectives that are preceded by
This declension pattern is also known as the third type or 'mixed' declension. See Wikipedia on German declension: http://en.wikipedia.org/wiki/German_declension#Attributive_adjectives