1 bài toán hay cần giải đáp

V

vansang02121998

tuananh8 said:
ta có: [TEX]2222 \equiv -4(mod7) ; 5555 \equiv 4(mod7) \Rightarrow2222^{5555}+5555^{2222} \equiv -4^{5555}+4^{2222} \equiv (mod7)[/TEX]
Mà [TEX]-4^{5555}+4^{2222}=-4^{2222}(4^{3333}-1)=-4^{2002}((4^3)^{111}-1)[/TEX]
[TEX]=-4^{2222}(64^{111}-1)[/TEX]
Mà [TEX]64^{111}-1=63(64^{110}+64^{109}+...+1)[/TEX] chia hết cho 7.
Suy ra [TEX]2222^{5555}+5555^{2222} \vdots 7[/TEX]
Bấm để xem đầy đủ nội dung ...


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