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2011-02-23 4:01 am

prove by MI ,THAT PROPOSITION IS TRUE
5^N-4^N-1 IS DIVISIBLE BY 4 FOR ALL POSITIVE INTEGERS N .

更新1:

http://img200.imageshack.us/i/73471814.png/

更新2:

http://img442.imageshack.us/i/75763934.png/ CAN U ALSO SOLVE THESE TWO PROBLEM

更新3:

http://hk.knowledge.yahoo.com/question/question?qid=7011022201507&mode=w&from=question&recommend=0&.crumb=j7gm/RkuCk8

回答 (1)

myisland8132

2011-02-23 4:10 am

✔ 最佳答案

Let P(n) be the statement " 5^N-4^N-1 IS DIVISIBLE BY 4"

When n = 1

5^1 - 4^1 - 1 = 0 is divisible by 4

P(1) is true

Assume that P(k) is true

i.e. 5^k - 4^k - 1 = 4M where M is a constant

When n = k + 1

5^(k+1) - 4^(k+1) - 1

=5(5^k - 4^k - 1) + 4^k + 4

= 4M + 4^k + 4

which is divisible by 4

So, P(k+1) is true

By MI, for all positive integer n, P(n) is true.

2011-02-22 22:12:08 補充：
I will try my best. By the way, I do not have enough space to type the answer at here. Please open these two questions in another place.

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