Chứng minh rằng : 24^ 1917+14^1917 chia hết cho 19
2 câu trả lời
$24^{1917} + 14^{1917}\\=(24^{1917} - 5^{1917}) + (14^{1917}+5^{1917})\\=(24-5)(...) + (14+5)(...)\\=19 (...) + 19 (...)\\=19 (...) \vdots 19\\\to 24^{1917} + 14^{1917}\vdots 19$
Ta có: 24 =5 (mod 19)
⇒241917 =51917 (mod 19)
14 =-5 (mod 19)
⇒141917 =-51917 (mod 19)
⇒241917 + 141917 =51917 + (-51917) (mod 19)
241917 +141917 =0 (mod 19)
hay 241917+ 141917 ⋮19 (đpcm)
