1a) Using the binomial theorem, expand (x+1)^77
b) Hence prove that when 88^77 is divided by 100, the remainder in 61
2 ) Using the binomial theorem, find the remainder when 8^88 is divided by each of the following integers.
a) 7
b) 49
F.4 Binomial Theorem
2010-02-23 4:48 am
回答 (1)
2010-02-23 6:15 am
✔ 最佳答案
88^77為偶數,除以100,餘數61為奇數????2010-02-22 22:15:14 補充：
1.
(a) (x+1)^77=C(77,0)+C(77,1)x+C(77,2)x^2+...+C(77,77)x^77
=1+77x+x^2*(....)
(b) 81^77=(80+1)^77
=1+77*80+80^2*(.....)
=6161+ 100*(...)
so that 81^77 is divided by 100 obtained the remainder 61
2.
8^88=(7+1)^88= 1+88*7+7^2*(....)
= 1+ 616+ 49*(...)
(a) 8^88 is divided by 7 the remainder is 1
(b) 1+616 divded by 49 the remainder is 29
收錄日期: 2021-04-13 17:06:53
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