Prove that we can find a positive integer n such that 7^n ends with 001.
更新1:
Ahem. 0 is not a positive integer. Read the question carefully PLEASE.
Very easy math! Help!
2009-08-18 5:23 pm
Please help me with the following question!
Prove that we can find a positive integer n such that 7^n ends with 001.
Prove that we can find a positive integer n such that 7^n ends with 001.
回答 (2)
2009-08-19 3:56 am
✔ 最佳答案
74 = 2401 = 2400 + 1(74)k = (2400 + 1)k
= ∑(r=0 to 2400) (kCr)2400r
Any terms higher than 24002 are multiples of 10000.
So ∑(r=0 to 2400)(kCr)2400r can be expressed as 10000N + 2400k + 1 where N is an integer.
It is obvious to see if k is a multiple of 5, the second last term is a multiple of 1000 leaving the whole sum a number with ending digits 001.
Indeed 720n satisfies the required condition for any positive integer n.
2009-08-18 5:41 pm
n=0 時 , 咩既 n 次都等於 1
收錄日期: 2021-04-23 14:35:34
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