Question

Chứng minh 8351⁶³⁴+8241¹⁴² chia hết cho 26

Answer 1

Ta có :
Đặt A = 8351\(^{634}\) + 8241\(^{142}\) = (8351\(^2\))\(^{317}\)+ 8241\(^{142}\)
Ta có:
8351 = 5 (mod 26) \(\Rightarrow\) 8351\(^2\) = 5\(^2\) = 25 = -1 (mod 26) \(\Rightarrow\) (8351\(^2\))\(^{317}\) = (−1)\(^{317}\) = -1 (mod 26)
8241 = -1 (mod 26) \(\Rightarrow\) 8241\(^{142}\) = (−1)\(^{142}\) = 1 (mod 26)
\(\Rightarrow\) A = (8351\(^2\))\(^{317}\) + 8241\(^{142}\) = -1 + 1 = 0 (mod 26) \(\Rightarrow\) A chia hết cho 26