Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/11)

Krystyna Bialek — Aleksander Grytczuk: The equation of Fermat in ...

- 82 with m positive integer then A

4

m + B

4t

o = C*

w , where A,B,C are matrices of the form A- [ a Í ]' »" [2 Ol C= [c S] 2. LEMMAS In the proofs of the theorems we can use the following lemmas: LEMMA 1 If I r s y m f R SI L ks r J [ kS R J for some n £ 2 then C4) R = \ [ (r+sVlTj

n + (r-s-/lT]

n ] , and 1 CS) s 2 vir [ (r+sVíTj" - (r-s-/"kT]

n ] . PROOF In case n=2 the Lemma can be seen directly and ana can complete the proof by mathematical induction on n. LEMMA 2 If A • [ c

a S ] with integers a,b,c,d, then for every integer n 2: 2