Teorija brojeva

Rezultati kolokvija održanog 25.4.2008.

Ime i prezime grupa Zad1 Zad2 Zad3 Zad4 Zad5 Zad6 Ukupno
Ivan Andrić D 10 10 0 0 0 10 30
Ivan Androš D 0 10 2 0 6 7 23
Valentino Antolković B 10 8 10 7 6 7 48
Stanko Arbutina - 0 0 0 0 0 0 0
Petar Babić A 10 10 10 6 1 10 47
Filip Bačić D 10 10 10 0 5 10 45
Mladen Badrov D 10 10 10 2 0 10 42
Kristina Bedeniković C 10 10 8 10 3 10 51
Marko Begić B 10 8 10 1 5 7 41
Đurđica Blažević A 10 3 5 0 0 0 18
Marina Borovnjak - 0 0 0 0 0 0 0
Andrea Bosak D 10 10 10 10 7 10 57
Marija Bošnjak C 10 9 10 5 10 10 54
Dubravka Božić C 10 10 9 5 5 10 49
Jana Buzolić D 10 9 10 2 6 10 47
Ivana Ciganović C 10 10 10 7 8 5 50
Krešimir Ciprić B 10 9 10 6 10 9 54
Ivana Colarić A 10 10 10 8 7 10 55
Josip Cvitanović A 10 5 10 1 3 4 33
Irena Dabić C 3 2 0 2 0 0 7
Martina Dorotek D 10 3 8 1 2 5 29
Martina Doz C 1 10 10 0 6 8 35
Ivana Duić B 10 10 10 2 10 8 50
Mirna Erceg A 10 10 8 5 5 10 48
Tamara Falak B 10 2 10 0 4 7 34
Ana-Marija Flegar A 10 10 10 9 8 10 57
Iva Gaćina B 2 8 8 8 9 7 42
Kristina Gašpić - 0 0 0 0 0 0 0
Tomislav Glavaš - 0 0 0 0 0 0 0
Stjepan Glibo D 10 10 5 5 1 0 31
Tena Gostović C 10 10 10 6 7 10 53
Irena Grbac A 10 1 5 0 0 7 23
Marko Gredičak B 5 1 8 10 3 7 34
Katarina Gudelj - 0 0 0 0 0 0 0
Ante Gunjača A 10 10 10 8 6 7 51
Ivana Gut - 0 0 0 0 0 0 0
Adnan Hamzabegović D 10 10 10 10 2 10 52
Marijan Han C 10 10 7 1 2 0 30
Slađana Herceg - 0 0 0 0 0 0 0
Ksenija Hodak B 10 10 9 10 7 10 56
Saša Ivanović - 0 0 0 0 0 0 0
Renata Jelić A 10 10 10 10 8 10 58
Marcela Jusup B 6 4 0 0 3 10 23
Matej Kadvolt - 0 0 0 0 0 0 0
Anđelka Kalfić D 10 10 8 0 0 0 28
Nena Kekez C 10 10 10 8 3 5 46
Ana Keller A 0 4 10 0 10 5 29
Stevo Kentrić B 10 5 9 0 0 1 25
Kristina Knežević D 10 10 1 1 0 0 22
Iva Kodrnja C 10 10 10 10 10 10 60
Vedran Kogej A 10 10 9 8 10 10 57
Valentina Koretić - 0 0 0 0 0 0 0
Maja Kovač B 10 9 8 4 5 0 36
Vedran Krnjaić - 0 0 0 0 0 0 0
Josipa Kunović D 10 8 10 5 6 1 40
Nenad Kuren - 0 0 0 0 0 0 0
Danijel Laklija C 10 10 10 10 10 10 60
Tomislav Lektorić - 0 0 0 0 0 0 0
Marija Lijović - 0 0 0 0 0 0 0
Ivana Major Šomođi C 10 2 10 4 1 7 34
Barbara Malkoč D 10 9 2 0 0 0 21
Anamaria Mandac B 10 10 10 8 10 10 58
Marko Marić A 10 10 9 3 5 1 38
Zoran Marinković - 0 0 0 0 0 0 0
Marina Marjanović-Zulim A 10 6 10 5 7 5 43
Goran Matijević C 10 3 10 0 8 8 39
Jasmin Matijević D 10 9 10 4 3 10 46
Hani Matulić A 10 10 10 8 8 0 46
Kristina Micak - 0 0 0 0 0 0 0
Mia Mijatović B 10 10 10 5 9 10 54
Martina Milaković A 10 9 10 0 3 0 32
Vesna Milenković - 0 0 0 0 0 0 0
Jelena Milojević C 10 10 10 0 8 10 48
Daniel Miočić D 10 10 10 10 9 8 57
Nikolina Morić B 10 10 10 2 9 7 48
Ivan Mušicki A 10 3 10 8 6 10 47
Josipa Nikolić E 10 10 10 10 8 10 58
Mia Nižić C 10 10 10 5 10 10 55
Adnana Nurikić D 10 10 10 10 10 10 60
Andrea Ostojić B 10 10 10 7 5 10 52
Mia Pamuković B 10 10 10 8 10 10 58
Jelena Patarčić C 10 10 10 2 9 6 47
Mihael Petrić D 10 10 10 5 7 10 52
Ivona Petrović A 10 10 10 10 6 8 54
Tina Petrović C 10 6 9 8 10 10 53
Igor Posavec A 10 10 10 10 5 10 55
Bojan Poturica - 0 0 0 0 0 0 0
Ana Prskalo B 10 10 9 5 3 10 47
Ana Radeljak D 10 10 9 1 1 10 41
Iva Radoš D 10 10 5 0 5 3 33
Vedran Rafaj C 10 10 10 1 6 8 45
Maja Rod A 10 10 10 0 2 3 35
Ivana Rogulj A 10 10 10 5 7 1 43
Maja Rogulja B 10 7 10 5 8 10 50
Dean Singer D 10 10 10 0 1 8 39
Anja Skendžić D 10 10 10 1 7 10 48
Ana Soldo - 0 0 0 0 0 0 0
Bernardica Solina D 10 10 8 0 0 5 33
Alenka Solje B 10 10 8 8 8 10 54
Denis Stažnik B 10 6 9 9 3 10 47
Željka Stojanac B 10 10 10 8 10 10 58
Sanja Stojanović A 10 3 9 3 3 10 38
Maja Šarić A 10 10 10 1 7 10 48
Marijana Šikić A 10 10 10 3 8 10 51
Nevenka Šistov - 0 0 0 0 0 0 0
Kristina Šoković C 10 10 10 0 5 0 35
Lana Špiljarić A 10 10 10 5 3 10 48
Mate Šunjić C 10 10 10 10 10 10 60
Matija Švenda A 10 5 10 4 2 5 36
Višnja Tenčić E 10 10 10 10 10 10 60
Ilija Tomaš D 10 10 10 4 10 10 54
Vinka Trevižan A 0 8 3 0 1 0 12
Tihana Trivić B 10 9 9 1 6 4 39
Ivana Turčić A 10 7 10 10 4 5 46
Kristina Ugarković C 10 10 10 7 10 10 57
Martina Ursa - 0 0 0 0 0 0 0
Dragutin Viher D 10 10 10 5 8 10 53
Marija Visković C 10 10 10 8 7 10 55
Ante Višić - 0 0 0 0 0 0 0
Dolores Vlašić C 10 10 10 8 8 10 56
Ana Vranešić A 10 2 10 3 8 4 37
Denis Vrdoljak A 10 9 10 8 0 1 38
Mirta Vučković - 0 0 0 0 0 0 0
Martina Vukelić A 10 10 10 8 10 10 58
Bernard Živković B 10 10 10 0 6 10 46
Ana Žoldin B 10 6 10 0 10 8 44

Zadaće se mogu pogledati u srijedu, 30.4.2008. u 14:15.

Rješenja zadataka:

grupa A
1. g = 21, x = 25, y = -56.
2. x ≡ 200, 427, 654 (mod 681)
3. x ≡ 4001 (mod 5083)
4. n = 15, 16, 20, 24, 30
5.a) Ima 24 primitivna korijena modulo 53; najmanji je 2. 5.b) x ≡ 28 (mod 53)
6. (58/401) = 1, (59/401) = -1

grupa B
1. g = 11, x = -73, y = 190.
2. x ≡ 77, 300, 523 (mod 669)
3. x ≡ 3001 (mod 5681)
4. n = 17, 32, 34, 40, 48, 60
5.a) Ima 28 primitivnih korijena modulo 59; najmanji je 2. 5.b) x ≡ 22 (mod 59)
6. (46/353) = 1, (47/353) = 1

grupa C
1. g = 13, x = -27, y = 55.
2. x ≡ 101, 244, 387, 530, 673 (mod 715)
3. x ≡ 1999 (mod 4807)
4. n = 19, 27, 38, 54
5.a) Ima 16 primitivnih korijena modulo 61; najmanji je 2. 5.b) x ≡ 25 (mod 61)
6. (41/307) = 1, (42/307) = 1

grupa D
1. g = 17, x = 19, y = -23.
2. x ≡ 24, 201, 378, 565, 732 (mod 885)
3. x ≡ 1001 (mod 7429)
4. n = 43, 49, 86, 98
5.a) Ima 20 primitivnih korijena modulo 67; najmanji je 2. 5.b) x ≡ 26 (mod 67)
6. (37/251) = -1, (38/251) = 1

Andrej Dujella