4^12除25後的remainder
回答 (3)
2009-06-03 7:55 pm
✔ 最佳答案
4^12= (4 x 4 x 4 x 4)^3= 256^3
= (250 + 6)^3
= 250^3 + 3 x 250^2 x 6 + 3 x 250 x 6^2 + 6^3
Since first 3 terms are divisible by 25, then remainder equals the remainder when 6^3 (= 216) is divided by 25. So the remainder is 16.
2009-06-03 6:45 pm
412 ≣ (43)4
≣ 644
≣ 144 (mod 25)
≣ (142)2
≣ 1962
≣ 212 (mod 25)
≣ 441
≣ 16 (mod 25)
≣ 644
≣ 144 (mod 25)
≣ (142)2
≣ 1962
≣ 212 (mod 25)
≣ 441
≣ 16 (mod 25)
參考: myself
2009-06-03 10:23 am
4^12 = 64^4 = 14^4 = 196^2 = 21^2 = 441 = 16(mod25)
so the remainder is 16.
so the remainder is 16.
收錄日期: 2021-04-22 00:33:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090603000051KK00160