標題:
數學問題 20分
發問:
(1) Find the smallest positive value of x such that (4x8+3x7+2x5+x) mod 5 = 0where x is known as the check digit of the 4-digit number 875x(2a) Show that √3 is an irrational number [use "Proof by contradiction"](b) Prove the follow statement by the method of "Proof by... 顯示更多 (1) Find the smallest positive value of x such that (4x8+3x7+2x5+x) mod 5 = 0 where x is known as the check digit of the 4-digit number 875x (2a) Show that √3 is an irrational number [use "Proof by contradiction"] (b) Prove the follow statement by the method of "Proof by contradicition" : THe difference between a rational and an irrational number is irrational (C) Find a counter example to disprove the following statement THe difference between two different irrational number is irrational (d) Given 12 integers, show that at least two of them can be chosen such that their difference is divisible by 11
最佳解答:
Refer to the previous answer below for Q2: https://hk.knowledge.yahoo.com/question/question?qid=7014103000015 2014-11-07 16:17:27 補充： (1) Let n be any positive integer (4x8+3x7+2x5+x) mod 5 = 0 (63+x) mod 5 = 0 63+x = 5n+0 x=5n-63 ≥ 0 (0≤x ≤9) n ≥ 63/5=12.6 n ≥13 (n is integer) n is smallest at the value of 13, hence smallest x=5(13)-63=2 The smallest positive value of x is 2.
You can ask us what you do not know, but you cannot ask us to help you do homwork!!!!!!!!!!!!!!!!!!!!|||||ITE3107 Assignment 2014/2015 Please do homework on your own :)
數學問題 20分
發問:
(1) Find the smallest positive value of x such that (4x8+3x7+2x5+x) mod 5 = 0where x is known as the check digit of the 4-digit number 875x(2a) Show that √3 is an irrational number [use "Proof by contradiction"](b) Prove the follow statement by the method of "Proof by... 顯示更多 (1) Find the smallest positive value of x such that (4x8+3x7+2x5+x) mod 5 = 0 where x is known as the check digit of the 4-digit number 875x (2a) Show that √3 is an irrational number [use "Proof by contradiction"] (b) Prove the follow statement by the method of "Proof by contradicition" : THe difference between a rational and an irrational number is irrational (C) Find a counter example to disprove the following statement THe difference between two different irrational number is irrational (d) Given 12 integers, show that at least two of them can be chosen such that their difference is divisible by 11
最佳解答:
Refer to the previous answer below for Q2: https://hk.knowledge.yahoo.com/question/question?qid=7014103000015 2014-11-07 16:17:27 補充： (1) Let n be any positive integer (4x8+3x7+2x5+x) mod 5 = 0 (63+x) mod 5 = 0 63+x = 5n+0 x=5n-63 ≥ 0 (0≤x ≤9) n ≥ 63/5=12.6 n ≥13 (n is integer) n is smallest at the value of 13, hence smallest x=5(13)-63=2 The smallest positive value of x is 2.
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其他解答:You can ask us what you do not know, but you cannot ask us to help you do homwork!!!!!!!!!!!!!!!!!!!!|||||ITE3107 Assignment 2014/2015 Please do homework on your own :)
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