## Elementarna teorija brojeva

### Rezultati kolokvija održanog 3.7.2009.

Zadaće se mogu pogledati u ponedjeljak, 13.7.2009. u 9 sati.

grupa A
1.   a) 275;   b) 2
2.   (29/571) = 1; (30/571) = 1
3.   (143, 24, 145), (143, 10224, 10225), (55, 132, 143), (143, 924, 935), (143, 780, 793)
4.   √300 = [17,3,8,3,34]
5.   (215, 12), (92449, 5160)
6.   Sn+1 = 4Sn - Sn-1; pri dijeljenju s 11, ponavljaju se ostaci: 4,3,8,7,9,7,8,3,4,2,4,3,...

grupa B
1.   a) 326;   b) 3
2.   (33/569) = 1; (34/569) = 1
3.   (119, 120, 169), (119, 7080, 7081), (105, 56, 119), (119, 1008, 1015), (119, 408, 425)
4.   √303 = [17,2,2,5,2,2,34]
5. (107, 6), (22897, 1284)
6.   Sn+1 = 14Sn - Sn-1; pri dijeljenju s 11, ponavljaju se ostaci: 3,7,7,3,2,3,7,...

grupa C
1.   a) 377;   b) 1
2.   (41/563) = -1; (42/563) = -1
3.   (247, 96, 265), (247, 30504, 30505), (247, 2340, 2353), (95, 228, 247), (247, 1596, 1615)
4.   √300 = [17,1,1,4,1,1,34]
5. (71, 4), (10081, 568)
6.   Sn+1 = 18Sn - Sn-1; pri dijeljenju s 11, ponavljaju se ostaci: 7,3,3,7,2,7,3,...

grupa D
1.   a) 426;   b) 1
2.   (37/557) = -1; (38/557) = -1
3.   (203, 396, 445), (203, 20604, 20605), (147, 140, 203), (203, 2940, 2947), (203, 696, 725)
4.   √314 = [17,1,2,1,1,2,1,34]
5. (53, 3), (5617, 318)
6.   Sn+1 = 16Sn - Sn-1; pri dijeljenju s 5, ponavljaju se ostaci: 1,4,3,4,1,2,1,4,...