Tìm số chính phương có bốn chữ số , biết rằng 2 chữ số đầu giống nhau và hai chữ số cuôí giống nhau
Bài viết đã được chỉnh sửa nội dung bởi nguyentrunghieua: 08-08-2011 - 21:52
Bài viết đã được chỉnh sửa nội dung bởi nguyentrunghieua: 08-08-2011 - 21:52
Học gõ công thức toán học tại đây
Hướng dẫn đặt tiêu đề tại đây
Hướng dẫn Vẽ hình trên diễn đàn toán tại đây
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Số phải tìm có dạng: $\overline {aabb} $ với $a,b \in N,1 \le a,b \le 9$.Bài 12
Tìm số chính phương có bốn chữ số , biết rằng 2 chữ số đầu giống nhau và hai chữ số cuôí giống nhau
Bài viết đã được chỉnh sửa nội dung bởi Phạm Quang Toàn: 09-08-2011 - 09:56
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”).
Học gõ công thức toán học tại đây
Hướng dẫn đặt tiêu đề tại đây
Hướng dẫn Vẽ hình trên diễn đàn toán tại đây
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Giải:Bạn gợi ý đi chứ bài này khó ghê
MÌnh xin đưa ra bài này mong mọi ng giúp
Cho $k$ N $k$ 0 và A là số có $2k$ chữ số 1, B là số có $k$ chữ số 2
C/m A-B là một số chính phương
$A = \underbrace {111...11}_{2k} = \dfrac{{10^{2k} - 1}}{9};\,\,\,\,\,\,B = \underbrace {222...22}_k = 2.\dfrac{{10^k - 1}}{9} = \dfrac{{2.10^k - 2}}{9}$
$\Rightarrow A - B = \dfrac{{10^{2k} - 1}}{9} - \dfrac{{2.10^k - 2}}{9} = \dfrac{{10^{2k} - 2.10^k + 1}}{9} = \left( {\dfrac{{10^k - 1}}{3}} \right)^2 $
$10^k - 1 = \underbrace {999...99}_k \vdots 3$
Gợi ý nhé! Bài này sao ta không thử áp dụng định lý Fermat nhỏ xem nào!Xin lỗi về việc nhầm đề bài 11, xin chữa lại như sau:
Bài 11: Tìm tất cả các số nguyên tố $p$ sao cho $2^{11p}-2$ chia hết cho $11p$.
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”).
$\dfrac{{\overline {ab} }}{{\overline {bc} }} = \dfrac{a}{c};\,\,\,\dfrac{{\overline {an} }}{{\overline {bn} }} = \dfrac{a}{b};\,\,....$
Thí dụ: $\dfrac{{26}}{{65}} = \dfrac{2}{5}$$\dfrac{{10a + n}}{{10b + n}};\,\,\dfrac{{10n + a}}{{10n + b}};\,\,\dfrac{{10n + a}}{{10b + n}};\,\,\,\dfrac{{10a + n}}{{10n + b}}$.
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”).
Bài viết đã được chỉnh sửa nội dung bởi ongdongheo: 01-09-2011 - 09:06
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”).
Bài viết đã được chỉnh sửa nội dung bởi Phạm Quang Toàn: 26-09-2011 - 18:07
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”).
Bài viết đã được chỉnh sửa nội dung bởi Phạm Quang Toàn: 17-10-2011 - 19:24
►|| The aim of life is self-development. To realize one's nature perfectly - that is what each of us is here for. ™ ♫
Bài 23: Cho đa thức bậc 6 $f(x)$
$$f(1) = f(-1); f(2)=f(-2); f(3)=f(-3)$$
Cmr: $f(x) =f(-x)$ với mọi $x$
Bài viết đã được chỉnh sửa nội dung bởi Phạm Quang Toàn: 01-01-2012 - 20:10
Bài viết đã được chỉnh sửa nội dung bởi Phạm Quang Toàn: 13-01-2012 - 17:17
Bài 20: Tìm tất cả các cặp số nguyên tố $(p;q)$ sao cho $p^2+7pq+q^2$ là 1 số chính phương.
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
Bài này dùng lùi vô hạn, dễ dàng tìm được nghiệm $(x,y,z)=(0,0,0)$.Bài 24:tìm nghiệm nguyên của hệ
$$x^2+2001y^2=z^2$$
$$2001x^2+y^2=t^2$$
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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