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13. príklad 1. zimnej série 2010/2011

Zadanie:
Prvočíslo $p$ dáva zvyšok jedna po delení štyrmi. Zjednodušte výraz

$$\sum_{k=1}^{\frac{p-1}{2}} \left\{ \frac{k^2}{p} \right\},$$

kde $\{x\}$ je desatinná časť $x$. Desatinná časť $x$ je daná predpisom $\{x\}=x-\lfloor x \rfloor$, kde $\lfloor x \rfloor$ je dolná celá časť $x$ (najväčšie celé číslo, ktoré nie je väčšie než $x$).



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no grgoslave je to jasne... tento vinekd si uzi ako len pojde a ja verim ze pojde :) spolocnost na to mat budes minimalne jeden vecer, neopovaz sa ju sprznit :) a next vinekd ides sem ku mne.. ja ta zoznamim s este jednou starou pannou co potrebuje prerazit.. je to projekt pre nas, co s nou robime s najvyssou prioritou..od pondelka zacinam sirit reci, ze sa s tebou vyspala aby si mal aj potrebnu inspiraciu...uz sa na teba tesim :)

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HRim7D3bZ8j <ytkownik~if~uj~edu~pl> - 06. 11. 2013 - 19:05:17 z 188.143.232.12
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r8mnGoHp <mblaszkowiak~wp~pl> - 06. 11. 2013 - 00:58:59 z 188.143.232.12
Оставьте свой комментарий Вы можете использовать следующие HTML тэги: <a> <abbr> <acronym> <b> <blockquote> <cite> <code> <del> <em> <i> <pre> <q> <strike> <strong> Notify me of followup cmmoents via e-mail

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qD1qOdNj3XO <skipatrol~madriverglen~com> - 05. 11. 2013 - 11:41:25 z 188.143.232.12
V prvom rade gratulujem Ondrovi k vitzsatvu, ale chcela by som pogratulovat aj vsetkym, ktori sa do sutaze zapojili, priklady boli velmi pekne :).A chcela by som sa podakovat aj tvorcovi sutaze, ze ma vzdy nejake super napady a uz sa tesim, na nejaky dalsi :).

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Fillippo - 14. 10. 2010 - 13:30:59 z 158.195.208.36
pepovi gratulujem, ze sa zaradil medzi dvoch uspesnych riesitelov tejto ulohy. Sysel, teba odkazujem, este pred zverejnenim vzorakov, na Legendrov symbol a Eulerove kriterium. S tym to uz urcite zvladnes dorazit. Inak to mozu byt este pre teba(aj pre inych) dakedy uzitocne veci v MO ale aj inde.

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Pepa - 13. 10. 2010 - 18:35:42 z 220.29.broadband10.iol.cz
Syseľ napísal:
Napríklad tam, že potrebujem dokázať $\; \forall A\in Z :\exists B\in Z : A^2+B^2 \equiv 0 \; mod \; p \;$ ?

Já jsem se odkázal na známé tvrzení, že -1 je kvadratický zbytek mod p, když p je 4k+1 ;-)

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Syseľ - 13. 10. 2010 - 16:39:20 z 193.87.175.2
Napríklad tam, že potrebujem dokázať $\; \forall A\in Z :\exists B\in Z : A^2+B^2 \equiv 0 \; mod \; p \;$ ?

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Fillippo <filip~sladek~gmail~com> - 11. 10. 2010 - 16:21:39 z 158.195.80.60
tak co drtici? kto si trufol? resp. dostal sa niekto aspon niekam?

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