Tìm số dư khi chia A cho 7 với A $= 10^{10}+10^{100}+10^{1000}+...+10^{1000000000}$
#2
Đã gửi 16-10-2013 - 17:13
Zaraki
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PQT
Ta có $10^{10} \equiv 3^{10} \equiv 9^5 \equiv 2^5 \equiv 2^2 \pmod{7}$.Tìm số dư khi chia A cho 7 với A $= 10^{10}+10^{100}+10^{1000}+...+10^{1000000000}$
Tương tự thì $10^{100} \equiv 2^2 \pmod{7}, \cdots$.
- MrJokerWTF yêu thích
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
#4
Đã gửi 16-10-2013 - 21:48
Zaraki
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PQT
Tại sao các số $2^{50}$ $2^{500}$ ... đều đồng dư vs $2^{2}$ vậy bạn ??
Vì $2^{3k} \equiv 1 \pmod{7}$ mà $50,500 \equiv 2 \pmod{3}$.
- perfectstrong và MrJokerWTF thích
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
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