My provincial exam #2

7 1 3 11 9

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1 solution

Thanh Viet
Feb 26, 2015

Bài này là bài 446 phần Đại số trong sách Nâng cao và Phát triển Toán 8, tập 2 của Vũ Hữu Bình :D

(No offense) :D

Trung Đặng Đoàn Đức - 6 years, 3 months ago

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Bài này là bài cho lớp 6 trên Tạp chí Toán học và Tuổi trẻ tháng 2.

Thanh Viet - 6 years, 3 months ago

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Lớp 8 nó là bài sao đấy :D

Trung Đặng Đoàn Đức - 6 years, 3 months ago

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@Trung Đặng Đoàn Đức Ừ. Vậy mà cho ng ta cho lớp 6 :v Tớ xem giải trong sách rồi, hay hơn cách của tớ nhỉ? :D

Thanh Viet - 6 years, 3 months ago

if x=1/2, and y=1, then, min A= 6-5= 1

AMAN KUMAR - 6 years, 3 months ago

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However, x x and y y are all integers.

Thanh Viet - 6 years, 3 months ago

Is there any method which does not use options? @Aryan Sanghi

Vinayak Srivastava - 2 months ago

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Actually I also did it using options. Also, I am kinda weak in number theory, so I won't be able to tell another solution. :)

Aryan Sanghi - 2 months ago

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Ok no problem let me ask @Mahdi Raza

Vinayak Srivastava - 2 months ago

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@Vinayak Srivastava I feel that this method is sufficient to show that 11 is the least difference since the ending digits are cyclic. There was no need to even know the options since there is no other outcome other than 5^y ending in 25 and 36^x ending in 16, 36, 56, 76 or 96. We can see that 36 - 25 is the current minimum, so we just need to check if ( 36 25 ) (\ldots36 - \ldots 25) is possible. And the solution has proven that it isn't possible because then 5^y must be div by 3, which isn't possible except y=0, but y>0

Mahdi Raza - 1 month, 4 weeks ago

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@Mahdi Raza Nice solution ✌️

Aryan Sanghi - 1 month, 4 weeks ago

@Mahdi Raza Thanks for the solution!

Vinayak Srivastava - 1 month, 4 weeks ago

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