tìm số dư trong phép chia 2008^201 cho 2003

H

hiensau99

Cái này phải dùng máy tính

[TEX] 2008^{201} \equiv 5^{201} \pmod{2003}[/TEX]
+ [TEX] 5^{5} \equiv 1122 \pmod{2003} [/TEX]
+[TEX] 5^{10} \equiv 1000 \pmod{2003} [/TEX]
+[TEX] 5^{20} \equiv 503 \pmod{2003} [/TEX]
+[TEX] 5^{40} \equiv 631 \pmod{2003} [/TEX]
+[TEX] 5^{80} \equiv 1567 \pmod{2003} [/TEX]
+[TEX] 5^{100} \equiv 5^{80}.5^{20} \equiv 1567.503 \equiv 1022 \pmod{2003} [/TEX]
+[TEX] 5^{200} \equiv 921 \pmod{2003} [/TEX]
+ [TEX] 5^{201} \equiv 921.5 \equiv 599 \pmod{2003} [/TEX]

Vậy [TEX]2008^{201}[/TEX] chia 2003 dư 599
 
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