pnfrf

Ol flzzrgel, jr fubhyq rkcrpg gur zbivrf jvgu uvturfg pevgvp fpberf gb unir ybjre nhqvrapr fpberf, naq ivpr irefn va obgu pnfrf sbe ybj/uvtu nhqvrapr fpber.

My attempt was similar, but I didn't zragvba gur rqtr pnfrf so I may not have received full credit from the grader (they don't tell you which question your points come from).

Gur pbhag bs cbyltbaf sebz guvf vf fvzcyl gur pbhag bs havdhr frgf bs 4-cbvagf ylvat ba fhpu erpgnatyrf (pbzovangbevny sbezhyn: ovt grez vf N^2 O^2 (bar ba rnpu rqtr -- # vf whfg gur cebqhpg bs rqtr yratguf), cyhf gur pnfrf jurer cnvef bs cbvagf ner ba gur fnzr rqtr (funer k- be l-) (cbffvoyl gjb cnvef -- guvax (2,0) (1,0) (0,1) (0,2)), zvahf gur pnfrf jurer gurl uvg gur fnzr pbeare).

Rahzrengvat gur pnfrf; nal sbhe cbvagf qrsvar n erpnagthyne "uhyy": [(zva n_k, znk_k)] K [zva n_l, znk n_l)] ('n' enatvat bire gur sbhe cbvagf) Va gur pnfrf bs vagrerfg (3) be (4), ng yrnfg guerr bs gur cbvagf yvr ba gur rkgrevbe rqtr bs guvf uhyy.

Rahzrengvat gur pnfrf; nal sbhe cbvagf qrsvar n erpnagthyne "uhyy": [(zva n_k, znk_k)] K [zva n_l, znk n_l)] ('n' enatvat bire gur sbhe cbvagf) Va gur pnfrf bs vagrerfg (3) be (4), ng yrnfg guerr bs gur cbvagf yvr ba gur rkgrevbe rqtr bs guvf uhyy.