kms - fórum o príkladoch

7. príklad 3. zimnej série 2008/2009

Zadanie:
Myrec sa hral na parkovisku s kriedou. Napadlo mu, že by si mohol písať na zem čísla. Keby ich písal zaradom, bolo by to nudné. Preto napísal na betón vedľa seba nejako poprehadzované čísla 1, 2, $\dots$ , 100. Dostal takto postupnosť čísel $a_1,\ a_2,\ \dots ,\ a_{100}$ . Táto postupnosť sa mu nepáčila, tak si znova zmyslel iné poradie tých istých čísel a opäť ich napísal vedľa seba. Dostal takto postupnosť čísel $b_1,\ b_2,\ \dots ,\ b_{100}$ . Stále sa mu to nepáčilo, ale vymýšľať novú postupnosť čísel sa mu tiež nechcelo. Zistil však niečo zaujímavé. Keď urobil súčiny $a_1b_1,\ a_2b_2,\ \dots ,\ a_{100}b_{100}$ , tak medzi nimi našiel také dva, že dávajú rovnaký zvyšok po delení číslom 100. Bola toto náhoda, alebo stalo by sa mu to, nech by postupnosti čísel zvolil akokoľvek?

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