Elementarna teorija brojeva

Rezultati kolokvija održanog 3.7.2009.

Ime i prezime grupa Zad1 Zad2 Zad3 Zad4 Zad5 Zad6 2. kol. 1. kol. zad. dod. Ukupno Ocjena
Dubravko Antunović B 9 0 10 10 6 0 35 52 20 0 107  
Jelena Artuković C 10 10 8 10 10 0 48 41 10 5 104  
Ivana Babić B 9 10 10 10 10 0 49 48 20 0 117  
Ivana Bačani A 10 5 5 10 7 0 37 43 17 0 97  
Vesna Bajs D 5 10 10 10 10 0 45 33 20 0 98  
Željka Bakmaz A 10 10 10 10 10 7 57 53 10 0 120  
Tihana Balažinec D 5 10 10 10 10 3 48 58 20 10* 136 5
Pavo Baničević A 1 0 0 0 0 0 1 11 10 0 22  
Jelena Baranović D 8 8 10 10 10 10 56 51 20 0 137  
Martina Barić D 5 10 10 10 10 5 50 47 20 0 117  
Željka Bendelja A 10 5 10 10 6 0 41 55 20 0 116  
Iva Bilić B 10 10 10 10 8 1 49 42 20 10* 121 4
Đurđica Blažević A 8 5 9 10 8 10 50 48 20 0 118  
Zrinka Božić C 10 10 10 10 10 1 51 45 20 15* 131 4
Tomislav Bubica B 8 5 10 1 0 1 25 21 0 0 46  
Antonija Capan C 6 8 10 10 8 0 42 45 20 10* 117 4
Tanja Cokarić B 7 0 10 10 10 0 37 32 20 0 89  
Ivana Crnković B 8 10 10 10 10 5 53 46 20 20* 139 5
Eleonora Crvenka B 8 10 10 10 9 5 52 50 17 15* 134 4
Josip Cvitanović C 5 5 10 10 10 9 49 42 20 0 111  
Luka Dragičević B 5 10 10 9 7 7 48 32 0 0 80  
Ivana Dugan C 10 5 10 10 6 0 41 33 20 10* 104 3
Ivana Dugorepec A 10 10 10 10 10 0 50 49 20 20* 139 5
Vlatka Dumić A 5 10 10 10 1 1 37 46 9 0 92  
Mario Erak A 8 4 10 10 1 1 34 53 20 0 107  
Tajana Fiolić -               31 15 0 46  
Stjepan Glibo B 5 10 7 10 10 0 42 38 0 0 80  
Barbara Goričanec C 10 10 10 10 10 9 59 58 20 5 142  
Marinela Hordov B 10 10 10 10 10 9 59 52 20 20* 151 5
Marko Horvat B 8 10 2 10 5 0 35 38 20 5 98  
Zoran Horvat C 8 10 7 10 10 0 45 50 20 10* 125 4
Diana Horvatović -               24 9 0 33  
Ivana Hranilović C 10 10 9 10 10 0 49 40 20 20* 129 4
Kristina Idžanović A 5 10 10 10 10 0 45   17 0 62  
Sarah Ivić -                 0 0 0  
Marina Ivkošić D 8 9 10 10 10 10 57 51 20 0 128  
Marijana Jozepović A 8 10 10 10 10 2 50 52 20 10* 132 4
Danijela Jurina D 10 10 10 10 10 1 51 56 20 20* 147 5
Edvin Kadić B 5 10 10 10 8 0 43 35 20 0 98  
Matej Kadvolt A 10 0 9 10 1 0 30 23 9 0 62  
Anastasija Kalaminec A 8 10 2 5 10 4 39 34 19 20* 112 4
Rahela Klenkar -               11 0 0 11  
Sara Kokot C 5 8 10 10 10 0 43 45 12 0 100  
Vlado Kopčić C 0 0 2 10 5 0 17 29 10 0 56  
Sanja Kopecki B 10 10 10 10 10 0 50 59 20 20* 149 5
Slađana Koprivnjak -                 0 0 0  
Vedran Kovačević C 5 0 10 10 10 0 35 30 0 0 65  
Jelena Kovačić B 10 10 10 10 10 1 51 52 20 10* 133 4
Ivana Kožić C 10 0 10 10 10 1 41 45 19 0 105  
Ana Kralj A 10 10 10 10 4 8 52 56 20 20* 148 5
Maja Kranjčec D 10 10 6 7 5 9 47 52 20 0 119  
Vedran Krnjaić A 10 8 10 1 0 0 29 38 20 0 87  
Iva Krsnik D 8 10 10 10 8 0 46 46 19 10* 121 4
Alan Kunštek B 9 9 0 10 5 5 38 46 20 10* 114 4
Maja Malounek C 10 10 10 10 10 10 60 57 20 20* 157 5
Josipa Mamić B 10 8 8 10 7 0 43 45 20 0 108  
Katarina Markač D 10 10 10 10 10 8 58 55 19 10* 142 5
Kristina Martinac -                 0 0 0  
Davor Mas C 10 10 10 10 0 1 41 58 20 15* 134 4
Katarina Medved D 10 2 10 10 10 2 42 35 18 10* 105 3
Monika Mihalić B 10 10 10 10 1 1 44 25 15 0 84  
Matija Milić -               48 20 0 68  
Marijana Milišić -             38 28 20 0 86  
Tamara Mlinar D 9 10 8 10 10 5 52 59 20 15* 146 5
Antonija Mohar D 10 10 2 10 0 0 32 42 20 0 94  
Klara Nesterović D 10 0 7 10 10 0 37 49 20 5 111  
Ante Nogalo A 5 10 10 10 0 0 35 37 19 0 91  
Maja Očko A 5 8 10 10 9 10 52 51 20 0 123  
Ivan Osman B 8 9 8 10 9 0 44 30 18 0 92  
Nikolina Panijan C 8 8 10 10 10 0 46 33 10 0 89  
Željko Patek D 5 10 8 10 8 0 41 43 20 10* 114 4
Dragana Paurević A 10 8 2 10 8 5 43 36 17 0 96  
Danijel Pavrlišak B 10 10 10 10 8 0 48 45 17 10* 120 4
Roni Pencinger C 8 10 0 0 10 1 29 42 11 0 82  
Josip Perić D 10 10 10 10 10 1 51 48 20 10* 129 4
Domagoj Perišić A 10 8 10 10 10 0 48 40 0 0 88  
Ivana Pinjuh B 10 10 10 10 10 9 59 36 20 0 115  
Ivana Plavčić C 10 10 10 10 10 0 50 45 20 0 115  
Slavena Popić D 8 10 7 10 10 0 45 43 20 10* 118 4
Petra Posavec D 0 0 1 0 0 0 1 28 0 0 29  
Filip Prelčec A 6 5 10 10 10 0 41 42 16 0 99  
Siniša Premužić B 10 10 8 10 10 0 48 52 18 0 118  
Igor Puček C 10 10 7 9 10 1 47 46 20 0 113  
Mario Puškarić D 10 10 7 8 4 0 48 53 20 10* 131 4
Nina Radin A 10 10 7 8 4 0 39 57 20 15* 131 4
Jelena Ribić B 10 10 10 10 10 10 60 56 20 20* 156 5
Marina Rom C 6 10 8 10 10 1 45 56 20 10* 131 4
Alen Romić -                 0 0 0  
Jelena Rozić D 10 10 10 10 7 0 47 51 17 0 115  
Antonija Rudež A 10 10 10 10 10 8 58 52 20 0 130  
Zorica Rupčić B 10 0 10 10 10 0 40 44 20 0 104  
Mateja Sabo C 9 0 2 10 10 0 31 39 20 15* 105 3
Tomislav Sente D 7 3 10 10 10 0 40 22 10 0 72  
Anja Sinadinović A 8 10 10 10 8 1 47 48 19 0 114  
Ivana Skorupan B 10 10 10 10 10 0 50 47 20 0 117  
Natalija Skupnjak C 10 8 8 10 5 0 41 49 20 0 110  
Ivana Slovic D 10 10 10 10 10 0 50 47 20 10* 127 4
Frane Sorić A 10 1 0 10 5 0 26 22 10 0 58  
Filip Srića B 10 10 2 10 8 2 42 35 20 15* 112 4
Mateja Šafarić C 8 10 10 10 10 10 58 56 20 20* 154 5
Tina Škrtić -               44 18 0 62  
Maja Šparica D 9 10 8 10 10 0 47 34 19 0 100  
Anamarija Štević A 5 2 10 10 2 0 29 43 19 0 91  
Jelena Štimac B 8 10 4 10 8 1 41 37 20 0 98  
Lovro Švenda C 9 6 7 6 5 0 33 35 20 0 88  
Kristina Tkalec D 8 8 9 10 7 0 42 47 17 0 106  
Tomislav Trabalko A 10 8 10 9 5 0 42 17 14 0 73  
Marin Vasiljevski B 4 10 10 10 10 0 44 50 20 0 114  
Sanja Violić C 10 10 7 10 10 0 47 51 20 15* 133 4
Ida Vlajsović D 10 5 10 10 10 0 45 42 20 0 107  
Matija Vrbanc C 6 10 10 10 10 0 46 40 18 10* 114 4
Ivan Vrbaški D 8 6 10 10 10 0 44 30 10 0 84  
Nikolina Aračić A 10 5 10 10 10 10 55 58 20 10* 143 5
Petar Bašić C 10 10 10 10 8 1 49 56 10 0 115  
Vesna Bučar -                 0 0 0  
Davor Bušić D 10 10 10 10 10 0 50   20 15* 85  
Maja Gaščić A 10 5 8 10 6 0 39 45 19 0 103  
Miroslav Grižić B 10 10 10 10 10 1 51   6 0 57  
Mažda Hdagha C 10 3 7 6 4 0 30 32 18 0 80  
Saša Hunjak B 10 10 10 10 10 1 51 55 20 20* 146 5
Katarina Kmezić B 10 10 10 10 10 0 50 58 20 10* 138 5
Danka Krivo C 10 10 10 10 9 10 59 40 20 20* 139 5
Ivana Martinić D 5 10 10 10 3 0 38 50 19 0 107  
Andreja Mikuš A 10 5 10 10 7 0 42 40 20 10* 112 4
Tanja Prhal D 6 8 10 10 10 0 44 47 20 10* 121 4
Dean Raonić D 10 5 5 5 5 0 30 30 20 0 80  
Ana Ružić A 10 10 10 10 10 10 60 57 20 20* 157 5
Ivana Šegrt D 10 10 2 9 6 7 44 43 20 20* 127 4
Antonio Tolić -                 0 0 0  
Hrvoje Vidaković C 5 10 4 10 10 10 49 36 0 0 85  
Jasna Vinković B 10 10 8 8 5 0 41 50 20 0 111  
Nedjeljko Žuvela C 10 7 8 0 0 0 25 29 20 0 74  
Janja Mikić D 9 0 0 1 0 0 10   0 0 10  

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

Rješenja zadataka:

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,...

Andrej Dujella