Lista 3

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Matema´tica Discreta I
Lista 03
01. Resolva as seguintes recurso˜es
(a) A0 = 2, A1 = 5, An+2 = 5An+1 − 6An
(b) B0 = 0, B1 = 3, Bn+2 = 7Bn+1 − 10Bn
(c) C0 = 2, C1 = 7, Cn+2 = 7Cn+1 − 12Cn
(d) D0 = 2, D1 = 2, Dn+2 = 2Dn+1 +Dn
(e) E0 = 2, E1 = 2, En+2 = 2En+1 − 2En
02. No algoritmo RSA, encontre o expoente decriptografador d para os seguintes mo´dulos m e expoentes
criptografadores e:
(a) m = 23 · 19, e = 13
(b) m = 7 · 19, e = 37
(c) m = 11 · 7, e = 29
(d) m = 17 · 19, e = 83
(e) m = 61 · 11, e = 23
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Respostas:
01. (a) An = 2
n + 3n (b) Bn = 5
n − 2n (c) Cn = 3n + 4n (d) Dn = (1 +
√
2)n + (1−√2)n
(e) En = (1 + i)
n + (1− i)n
02. (a) d = 61 (b) d = 73 (c) d = 29 (d) d = 59 (e) d = 287