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Re: [obm-l] Re: [obm-l] Re:[obm-l] Teoria dos n�meros
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] Re: [obm-l] Re:[obm-l] Teoria dos n�meros
- From: "Lucas Prado Melo" <lukepadawan@xxxxxxxxx>
- Date: Sat, 28 Apr 2007 07:27:12 -0300
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> Amigos, ajude-me nessas
quest�es:
> 1) Ache o menor n�mero natural terminado em
56, divis�vel por 56, e com a soma dos seus algarismos igual a 56.
Ok ...
Temos que 56 k == 56 (mod 100) => 56k - 56 == 0 (mod 100) => 56(k-1) == 0 (mod 100)
ok, 56 = 7 x 2^3, para 100 dividir 56(k-1) = 2^3x7x(k-1), 25 precisa dividir k-1. O menor caso � quando k-1 � igual a 25, logo k = 26.
Nosso n�mero, portanto � 56x26 = 1456