toán violympic 8 vòng 12

S

soccan

Đặt $A=51^{39}+39^{51}+2$
Có $A \equiv 132651^{13}+59319^{17}+2 \equiv 81^{13}+9^{17}+2 \equiv 9^{17}(9^9+1)+2 \equiv 9^{16}.9.10+2 \equiv 2\ (mod\ 90)$
Vậy $A$ chia $90$ dư $2$
 
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