ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ,, ᠳᠠᠰᠭᠠᠯ ᠶᠢᠰᠦ ᠮᠡᠳᠡᠯᠭᠡ ᠶᠢᠨ ᠪᠠᠳᠤᠳᠬᠠᠯ 1᠂ ᠰᠣᠩᠭᠤᠬᠤ ᠰᠡᠳᠤᠪ ① ᠳᠠᠷᠠᠭᠠᠬᠢ ᠬᠡᠯᠡᠯᠭᠡ ᠠᠴᠠ ᠳᠠᠰᠢᠶ᠎ᠠ ᠪᠣᠯᠬᠤ ᠨᠢ ︵D︶ A ᠣᠨᠤᠯᠳᠠ ᠬᠡᠳᠡᠭ ᠨᠢ ᠰᠢᠭᠦᠮᠵᠢ ᠵᠣᠬᠢᠶᠠᠯ ᠳᠠᠬᠢ ᠵᠣᠬᠢᠶᠠᠭᠴᠢ ᠶᠢᠨ ᠶᠠᠷᠢᠵᠤ ᠢᠯᠡᠳᠭᠡᠬᠦ ᠬᠡᠰᠡᠨ ᠦᠵᠡᠯᠳᠡ ᠪᠣᠯᠤᠨ᠎ᠠ᠃ B ᠣᠨᠤᠯᠳᠠ ᠶᠢ ᠳᠤᠷᠠᠳᠤᠭᠰᠠᠨ ᠰᠢᠯᠳᠠᠭᠠᠨ ᠪᠤᠶᠤ ᠦᠨᠳᠤᠰᠤᠯᠠᠯ ᠢ ᠪᠠᠷᠢᠮᠳᠠ ᠬᠡᠳᠡᠭ᠃ C ᠨᠤᠳᠠᠯᠠᠯᠳᠠ ᠬᠢᠬᠦ ᠬᠡᠳᠡᠭ ᠨᠢ ᠣᠨᠤᠯᠳᠠ ᠪᠠ ᠪᠠᠷᠢᠮᠳᠠ ᠶᠢ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠳᠠᠰᠭᠠᠯ ᠳᠣᠯᠤᠭ᠎ᠠ ᠮᠡᠳᠡᠯᠭᠡ ᠶᠢᠨ ᠪᠠᠳᠤᠳᠬᠠᠯ 1᠂ ᠰᠣᠩᠭᠤᠬᠤ ᠰᠡᠳᠤᠪ ① ᠵᠥᠪ ᠭᠠᠯᠢᠭᠯᠠᠭᠰᠠᠨ ᠨᠢ ︵B︶ A ᠭᠠᠷᠠᠭ\s1 ᠦᠶ᠎ᠡ ᠪᠠᠷ ᠤᠩᠰᠢᠨ᠎ᠠ᠃ B ᠵᠤᠯ\s4 ᠦᠶ᠎ᠡ ᠪᠠᠷ ᠤᠩᠰᠢᠨ᠎ᠠ᠃ C ᠬᠢᠮᠠᠭᠠᠳᠠᠬᠤ\s3 ᠦᠶ᠎ᠡ ᠪᠠᠷ ᠤᠩᠰᠢᠨ᠎ᠠ᠃ D ᠬᠠᠯᠠᠭᠠᠰᠤᠨ\s1 ᠦᠶ᠎ᠡ ᠪᠠᠷ ᠤᠷᠳᠤᠳᠬᠠᠵᠤ ᠤᠩᠰᠢᠨ᠎ᠠ᠃ ② ᠠᠳᠠᠯᠢ ᠨᠢᠭᠡᠨ ᠲᠠᠢᠨ ᠢᠯᠭᠠᠯ ᠤᠨ ᠬᠤᠪᠢᠯᠦᠯ ᠤᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠪᠠᠷ ᠪᠠᠢᠭ᠎ᠠ ᠦᠭᠡᠰ ᠤᠨ ᠪᠦᠯᠦᠭ ᠨᠢ᠄ ︵B︶ A ᠬᠤ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠳᠠᠰᠭᠠᠯ ᠲᠠᠪᠤ ᠮᠡᠳᠡᠯᠭᠡ ᠶᠢᠨ ᠪᠠᠳᠤᠳᠬᠠᠯ 1᠂ ᠰᠣᠩᠭᠤᠬᠤ ᠰᠡᠳᠤᠪ ① ᠲᠠᠰᠢᠶᠠᠷᠠᠭᠰᠠᠨ ᠬᠡᠯᠡᠯᠭᠡ ᠪᠣᠯᠬᠤ ᠨᠢ᠄ ︵D︶ A᠂ ᠪᠣᠭᠤᠨᠢ ᠡᠭᠡᠰᠢᠭ ᠪᠣᠯᠤᠨ ᠤᠷᠳᠤ ᠡᠭᠡᠰᠢᠭ ᠨᠢ ᠶᠠᠷᠢᠶᠠᠨ ᠤ ᠬᠡᠯᠡᠨ ᠲᠤ ᠤᠳᠭ᠎ᠠ ᠢᠯᠭᠠᠬᠤ ᠦᠢᠯᠡᠳᠤᠯ ᠲᠠᠢ ᠪᠠᠢᠳᠠᠭ᠃ B᠂ ᠨᠢᠭᠡ ᠦᠶ᠎ᠡ ᠲᠤ ᠤᠭᠰᠠᠷᠠᠨ ᠣᠷᠤᠭᠰᠠᠨ ᠬᠤᠶᠠᠷ ᠥᠭᠡᠷ᠎ᠡ ᠡᠭᠡᠰᠢᠭ ᠢ ᠬᠤᠣᠰ ᠡᠭᠡᠰᠢᠭ ᠬᠡᠳᠡᠭ᠃ C᠂ ᠮᠣᠩᠭᠤᠯ ᠬᠡᠯᠡᠨ ᠤ ᠥᠭᠡ ᠶᠢᠨ ᠨᠢᠬᠡᠳᠤᠬᠡᠷ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠡᠭᠡᠰ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ , ᠮᠠᠨᠳᠤᠬᠠᠢ ᠰᠡᠴᠡᠨ , ᠨᠣᠮ ᠤᠩᠰᠢᠬᠤ ᠬᠥᠳᠡᠯᠭᠡᠭᠡᠨ , ᠥᠨᠥᠳᠦᠷ ᠤᠨ ᠲᠠᠨᠢᠯᠴᠠᠭᠤᠯᠬᠤ ᠨᠣᠮ , ᠨᠢᠭᠡ᠂ ᠵᠣᠬᠢᠶᠠᠭᠴᠢ ᠶᠢᠨ ᠲᠤᠬᠠᠢ ᠲᠠᠨᠢᠯᠴᠠᠭᠤᠯᠭ᠎ᠠ ᠱ᠊᠂ ᠨᠠᠴᠤᠭᠳᠣᠷᠵᠢ\sᠪᠥᠬᠦᠳᠡ ᠨᠠᠶ᠋ᠢᠷᠠᠮᠳᠠᠬᠤ ᠳᠤᠮᠳᠠᠳᠤ ᠠᠷᠠᠳ ᠤᠯᠤᠰ ᠤᠨ ᠤᠯᠤᠰ ᠤᠨ ᠬᠤᠣᠰ ᠱᠠᠩᠨᠠᠯ ᠬᠦᠷᠳᠡᠭᠴᠢ᠂ ᠨᠡᠷ᠎ᠡ ᠬᠦᠨᠳᠦᠲᠦ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨᠲᠠᠨ᠂ ᠲᠡᠦᠬᠡᠴᠢᠨ᠃ 1936 ᠣᠨ ᠲᠤ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠰᠤᠳᠤᠯᠭᠠᠨ ᠤ ᠭᠠᠵᠠᠷ ᠤᠨ ᠲᠡᠦᠬ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄     ,  ,        ,1             ,            ,           

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄          1                      2               

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄       ,   1                 2                  

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄        1935 10                                       

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ PNBSP︔ ᠮᠣᠩᠭᠤᠯ ᠹᠢᠯᠢᠮ ᠤᠨ ᠳᠡᠪᠢᠰᠭᠡᠷ ᠵᠢᠷᠤᠭ /P

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠳᠡᠭᠷᠢ ᠠᠭᠤᠯᠠ ᠶᠢᠨ ᠥᠩᠭᠡ ᠦᠵᠡᠮᠵᠢ,ᠪᠢ ᠶᠧ,LIXIULAN,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠲᠠ᠄ ᠠᠶᠠᠨ ᠤ᠋ ᠴᠢᠭᠯᠡᠯ ᠳ᠋ᠡᠬᠢ ᠦᠵᠡᠮᠵᠢ ᠪᠣᠳᠠᠰ ᠢ᠋ ᠰᠣᠨᠢᠷᠬᠠᠬᠤ ᠢ᠋ᠢᠨ ᠳᠠᠭᠠᠤ ᠣᠨᠴᠠᠯᠢᠭ ᠰᠢᠨᠵᠢ ᠵᠢ ᠣᠯᠵᠤ᠂ ᠳᠠᠭᠠᠯᠳᠤᠭᠰᠠᠨ ᠰᠡᠳᠭᠢᠭᠳᠡᠯ ᠢ᠋ ᠰᠡᠷᠡᠵᠤ ᠣᠢᠯᠠᠭᠠᠶ᠎ᠠ᠃ ᠦᠵᠡᠮᠵᠢ ᠪᠣᠳᠠᠰ ᠤ᠋ᠨ ᠣᠨᠴᠠᠯᠢᠭ ᠰᠢᠨᠵᠢ ᠵᠢ ᠠᠳᠭᠤᠵᠤ᠂ ᠦᠵᠡᠭᠳᠡᠯ ᠠ᠋ᠴᠠ ᠰᠡᠳᠭᠢᠭᠳᠡᠯ ᠡᠭᠦᠰᠬᠦ ᠪᠢᠴᠢᠯᠭᠡ ᠢ᠋ᠢᠨ ᠠᠷᠭ᠎ᠠ ᠵᠢ ᠡᠵᠡᠮᠰᠢᠵᠤ ᠰᠤᠷᠤᠶ᠎ᠠ᠃ ᠡᠬᠡ ᠤ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 914 ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠤᠨ ᠥᠷᠭᠡᠳᠭᠡᠯ ᠪᠠ ᠰᠥᠪᠡᠭᠴᠢᠯᠡᠯ,ᠬᠡᠷᠪᠡ 𝑎𝑏 ᠪᠣᠯ᠂ ᠳᠠᠷᠭᠠᠠᠬᠢ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠠᠴᠠ ᠪᠠᠢᠭᠤᠯᠤᠭᠳᠠᠬᠤ ᠨᠢ\s,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ ᠄,𝐴 𝑎 𝑐 2 𝑏 𝑐 2,𝐵 𝑎− 𝑐 2 𝑏− 𝑐 2,𝐶 𝑎 𝑐 2 𝑏 𝑐 2,𝐷 𝑎 𝑐 2 1 𝑏 𝑐 2 1,ᠬᠡᠷᠪᠡ 𝑎𝑏 ᠪᠣᠯ᠂ ᠳᠠᠷᠭᠠᠠᠬᠢ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠠᠴ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 913 ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠢ ᠠᠰᠢᠭᠯᠠᠵᠤ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢ ᠪᠣᠳᠤᠬᠤ,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠲᠠ ᠄,ᠳᠡᠡᠭᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠢ ᠬᠡᠷᠡᠭ᠍ᠯᠡᠨ ᠲᠥᠭᠥᠮ ᠳᠡᠡᠭᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠵᠢ ᠪᠤᠳ᠋ᠤᠬᠤ ᠵᠢᠴᠢ ᠬᠠᠷᠢᠭᠤ ᠴᠤᠭᠯᠠᠷᠠᠯ ᠢ ᠨᠢ ᠳᠤᠭᠠᠨ ᠤ ᠲᠡᠩᠭᠡᠯᠢᠭ ᠳᠡᠭᠡᠷ᠎ᠡ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠵᠤ ᠴᠢᠳ᠋ᠠᠬᠤ ᠃,1 𝑎＜𝑏 𝑎−1____𝑏−1 2 𝑎𝑏 𝑎1 ___ 𝑏1

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 912 ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠲᠠ ᠄,1 ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠢ ᠮᠥᠷᠳᠡᠬᠦ ᠪᠠᠷ ᠳᠠᠮᠵᠢᠨ ᠳᠡᠡᠭᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠢ ᠡᠵᠡᠮᠰᠢᠬᠦ ᠃ 2ᠳᠡᠡᠭᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠪᠤᠯᠤᠨ ᠳᠡᠡᠭᠴᠡᠳᠬᠡᠯ ᠦᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠤᠨ ᠠᠳ᠋ᠠᠯᠢ ᠪᠤᠰᠤ ᠵᠢ ᠠᠡᠭ᠍ᠬ᠎᠎ᠠ ᠠᠯᠬᠤᠮ ᠲᠠᠨᠢᠬᠤ᠃,,1 𝑥3＞6,2 2𝑥＜8,ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 911 ᠲᠡᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠵᠢᠴᠢ ᠲᠡᠭᠦᠨ ᠦ ᠬᠠᠷᠢᠭᠤ ᠴᠤᠭᠯᠠᠷᠠᠯ,1 ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠤᠬᠠᠠᠠᠳ᠋ᠠᠬᠤᠨ ᠢ ᠤᠢᠯᠠᠭᠠᠨ᠎᠎ᠠ ᠃ 2 ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠪᠠ ᠬᠠᠷᠢᠭᠤ ᠴᠤᠠᠠᠯᠠᠷᠠᠯ ᠢ ᠲᠤᠳ᠋ᠤ ᠤᠢᠯᠠᠭᠠᠬᠤ᠃ 3 ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠴᠤᠠᠠᠯᠠᠷᠠᠯ ᠢ ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩᠭᠡᠯᠢᠭ ᠳᠡᠭᠡᠷ᠎ᠡ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠵᠦ ᠴᠢᠳ᠋ᠠᠬᠤ ᠃,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠳ᠋ᠠ ᠄,ᠨᠡᠷᠡᠳ᠋ᠦ ᠰᠠᠠᠠᠰᠤᠨ ᠪᠦᠮᠪᠦ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ 84 ᠭᠤᠷᠪᠠᠨ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠥᠯᠥᠭ ᠦᠨ ᠪᠣᠳᠣᠬᠤ ᠠᠷᠭ᠎ᠠ,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠳ᠋ᠠ ᠄,1ᠭᠤᠷᠪᠠᠨ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ᠌ ᠤᠨ ᠤᠬᠠᠠᠠᠳ᠋ᠠᠬᠤᠨ ᠢ ᠤᠢᠯᠠᠭᠠᠵᠤ ᠮᠡᠳ᠋ᠡᠭᠦ ᠃ 2 ᠬᠢᠯᠪᠠᠷ ᠭᠤᠷᠪᠠᠨ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ᠌ ᠢ ᠪᠤᠳ᠋ᠤᠵᠤ