特例独行的杂碎
幼苗
共回答了22个问题采纳率:81.8% 举报
1)∵(51,221)=17 (符号(51,221)表示51与221的最大公约数,以下类同)
且17│85 (符号17│85表示17整除85,以下类同)
∴51x≡85(221)有解
∵51x≡85(221)==>17*3x≡5*17 (13*17)
==>3x≡5 (13)
∵3x≡5 (13) ==>4*3x≡4*5 (13)
==>(13-1)x≡26-6 (13)
==>-x≡-6 (13)
==>x≡6 (13)
∴3x≡5 (13)的解是x≡6 (13)
故51x≡85(221)的所有解是
x≡6,19,32,45,58,71,84,97,110,123,136,149,162,175,188,201,214 (221);
2)∵(143,121)=11,且11不能整除501
∴143X≡501 (121)无解;
3)∵x≡572(77)==>x≡7*77+33(77)
==>x≡33 (77)
∴x≡572(77)的解是x≡33 (77);
4)∵(161,253)=23,且23│2300
∴161x≡2300 (253)有解
∵161x≡2300 (253)==>23*7x≡23*100 (23*11)
==>7x≡100 (11)
==>7x≡9*11+1 (11)
==>7x≡1 (11)
==>(11-4)x≡1 (11)
==>-4x≡1 (11)
==>4x≡-1 (11)
==>3*4x≡-3 (11)
==>(11+1)x≡-3 (11)
==>x≡-3 (11)
==>x≡8 (11)
∴7x≡100 (11)的解是x≡8 (11)
故161x≡2300 (253)的所有解是
x≡8,19,30,41,52,63,74,85,96,107,118,129,140,151,162,173,
184,195,206,217,228,239,250 (253).
1年前
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