Elementarna teorija brojeva

Rezultati kolokvija održanog 30.4.2009.

Ime i prezime grupa Zad1 Zad2 Zad3 Zad4 Zad5 Zad6 Ukupno
Dubravko Antunović A 10 8 10 7 7 10 52
Jelena Artuković D 10 10 10 7 4 0 41
Ivana Babić A 10 8 10 4 6 10 48
Ivana Bačani B 10 9 10 1 10 3 43
Vesna Bajs A 10 10 10 0 3 0 33
Željka Bakmaz B 10 10 10 6 10 7 53
Tihana Balažinec C 10 10 10 8 10 10 58
Pavo Baničević B 10 1 0 0 0 0 11
Jelena Baranović -              
Martina Barić C 10 10 10 7 10 0 47
Željka Bendelja D 10 10 10 5 10 10 55
Iva Bilić C 10 8 10 5 4 5 42
Đurđica Blažević D 10 10 10 5 8 5 48
Zrinka Božić D 10 10 10 6 8 1 45
Tomislav Bubica A 3 4 2 2 0 10 21
Antonija Capan B 10 10 10 5 0 10 45
Tanja Cokarić A 10 6 10 5 0 1 32
Ivana Crnković D 10 10 10 6 0 10 46
Eleonora Crvenka C 10 10 10 6 10 4 50
Josip Cvitanović A 10 10 8 5 4 5 42
Luka Dragičević A 10 3 9 0 0 10 32
Ivana Dugan D 10 10 10 0 3 0 33
Ivana Dugorepec B 10 10 10 5 9 5 49
Vlatka Dumić B 10 10 10 3 3 10 46
Mario Erak C 10 10 10 7 9 7 53
Tajana Fiolić D 10 10 8 0 0 3 31
Stjepan Glibo C 10 10 10 7 0 1 38
Barbara Goričanec C 10 10 10 10 10 8 58
Marinela Hordov A 10 10 10 9 10 3 52
Marko Horvat C 10 7 10 1 5 5 38
Zoran Horvat B 10 8 10 3 9 10 50
Diana Horvatović D 10 10 4 0 0 0 24
Ivana Hranilović D 10 7 8 5 10 0 40
Kristina Idžanović -              
Sarah Ivić -              
Marina Ivkošić C 10 10 10 1 10 10 51
Marijana Jozepović A 10 8 10 4 10 10 52
Danijela Jurina B 10 10 10 6 10 10 56
Edvin Kadić D 10 8 10 4 0 3 35
Matej Kadvolt B 10 3 10 0 0 0 23
Anastasija Kalaminec A 10 9 10 1 3 1 34
Rahela Klenkar C 5 4 0 0 0 2 11
Sara Kokot B 10 10 10 0 10 5 45
Vlado Kopčić A 10 10 9 0 0 0 29
Sanja Kopecki A 10 10 10 9 10 10 59
Slađana Koprivnjak -              
Vedran Kovačević C 8 7 10 0 0 5 30
Jelena Kovačić B 10 10 10 4 8 10 52
Ivana Kožić D 10 10 9 6 0 10 45
Ana Kralj C 10 10 10 6 10 10 56
Maja Kranjčec D 10 10 10 5 7 10 52
Vedran Krnjaić D 10 8 10 10 0 0 38
Iva Krsnik C 10 10 10 6 10 0 46
Alan Kunštek D 10 10 10 5 3 8 46
Maja Malounek A 10 10 10 7 10 10 57
Josipa Mamić C 10 10 10 5 10 0 45
Katarina Markač D 10 10 10 5 10 10 55
Kristina Martinac -              
Davor Mas A 10 10 10 8 10 10 58
Katarina Medved C 10 10 10 0 0 5 35
Monika Mihalić C 10 7 4 2 0 2 25
Matija Milić D 10 10 10 0 8 10 48
Marijana Milišić A 10 9 3 2 3 1 28
Tamara Mlinar B 10 10 9 10 10 10 59
Antonija Mohar C 10 7 10 8 0 7 42
Klara Nesterović A 10 10 10 1 8 10 49
Ante Nogalo A 8 10 8 0 1 10 37
Maja Očko B 10 8 10 4 9 10 51
Ivan Osman D 10 7 10 3 0 0 30
Nikolina Panijan A 10 10 10 1 2 0 33
Željko Patek D 8 10 10 2 3 10 43
Dragana Paurević D 10 6 10 7 3 0 36
Danijel Pavrlišak D 10 10 10 5 0 10 45
Roni Pencinger C 10 4 10 7 1 10 42
Josip Perić C 10 10 9 6 8 5 48
Domagoj Perišić B 10 10 10 0 0 10 40
Ivana Pinjuh B 10 4 8 4 10 0 36
Ivana Plavčić C 10 10 10 5 0 10 45
Slavena Popić A 10 10 10 3 10 0 43
Petra Posavec B 8 7 8 0 4 1 28
Filip Prelčec B 10 10 10 4 8 0 42
Siniša Premužić C 10 10 10 2 10 10 52
Igor Puček C 10 3 10 3 10 10 46
Mario Puškarić D 10 10 10 3 10 10 53
Nina Radin A 10 10 10 7 10 10 57
Jelena Ribić A 10 10 10 7 9 10 56
Marina Rom A 10 10 10 9 7 10 56
Alen Romić -              
Jelena Rozić A 10 10 10 8 3 10 51
Antonija Rudež A 10 10 8 4 10 10 52
Zorica Rupčić D 10 10 10 6 0 8 44
Mateja Sabo B 10 10 10 5 3 1 39
Tomislav Sente D 10 10 2 0 0 0 22
Anja Sinadinović C 10 7 10 6 7 8 48
Ivana Skorupan B 10 10 8 6 10 3 47
Natalija Skupnjak B 10 7 10 3 9 10 49
Ivana Slovic D 10 9 10 8 0 10 47
Frane Sorić C 10 8 4 0 0 0 22
Filip Srića B 10 3 10 2 0 10 35
Mateja Šafarić D 10 10 10 6 10 10 56
Tina Škrtić A 10 10 10 4 0 10 44
Maja Šparica A 10 8 7 5 3 1 34
Anamarija Štević B 10 10 10 4 8 1 43
Jelena Štimac C 10 10 10 0 7 0 37
Lovro Švenda A 8 3 10 3 1 10 35
Kristina Tkalec B 10 7 10 7 3 10 47
Tomislav Trabalko C 8 4 5 0 0 0 17
Marin Vasiljevski B 10 6 10 4 10 10 50
Sanja Violić D 10 10 10 6 10 5 51
Ida Vlajsović C 10 10 10 6 0 6 42
Matija Vrbanc D 10 10 10 0 0 10 40
Ivan Vrbaški D 10 8 6 6 0 0 30
Nikolina Aračić C 10 10 10 8 10 10 58
Petar Bašić D 10 10 10 6 10 10 56
Vesna Bučar -              
Davor Bušić -              
Maja Gaščić C 10 10 10 5 10 0 45
Miroslav Grižić -              
Mažda Hdagha D 10 10 4 1 7 0 32
Saša Hunjak D 10 10 10 5 10 10 55
Katarina Kmezić A 10 10 10 8 10 10 58
Danka Krivo A 10 8 10 2 0 10 40
Ivana Martinić B 10 10 10 7 3 10 50
Andreja Mikuš B 10 10 4 3 10 3 40
Tanja Prhal B 10 10 10 4 3 10 47
Dean Raonić D 10 5 10 5 0 0 30
Ana Ružić B 10 10 10 7 10 10 57
Ivana Šegrt D 10 5 10 5 3 10 43
Antonio Tolić -              
Hrvoje Vidaković A 10 2 10 4 0 10 36
Jasna Vinković A 10 10 10 4 6 10 50
Nedjeljko Žuvela B 10 9 10 0 0 0 29

Zadaće se mogu pogledati u petak, 8.5.2009. u 13:30.

Rješenja zadataka:

grupa A
1.   g = 13, x = -18, y = 25
2.   x ≡ 21, 238, 455 (mod 651)
3.   x ≡ 3737 (mod 5423)
4.   n = 15, 16, 20, 24, 30
5.   x ≡ 106, 233 (mod 343)
6.   a = 9, b = 5, c = 0, d = 1

grupa B
1.   g = 17, x = -87, y = 128
2.   x ≡ 200, 427, 654 (mod 681)
3.   x ≡ 4141 (mod 7163)
4.   n = 17, 32, 34, 40, 48, 60
5.   x ≡ 17, 323 (mod 343)
6.   traženi brojevi su 15789 i 15798

grupa C
1.   g = 19, x = -64, y = 93
2.   x ≡ 78, 325, 572 (mod 741)
3.   x ≡ 5252 (mod 6061)
4.   n = 19, 27, 38, 54
5.   x ≡ 39, 299 (mod 343)
6.   brojevi s traženi svojstvom su 4104, 8100, 9108

grupa D
1.   g = 23, x = -50, y = 77
2.   x ≡ 67, 306, 545 (mod 717)
3.   x ≡ 1919 (mod 6851)
4.   n = 43, 49, 86, 98
5.   x ≡ 124, 213 (mod 343)
6.   traženi sedmeroznamenkasti brojevi su 2111112, 1211112, 1121112, 1112112 i 1111212

Andrej Dujella