Even and Odd Numbers

b^{3} = 3375 = 15^{3} => b = 15 => a = 13 ; c = 17 => ac = 221
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b^{3} = 3375
=> b = \(\sqrt[3]{3375}=15\)
Because a,b,c are three consecutive odd number and b = 15 so
a = 13 ; b = 15 ; c = 17
ac = 15 . 17 = 221


FA KAKALOTS 09/02/2018 at 22:06
1 is odd,so the 3rd number is even
=> The 4th number is odd and so is the 5th number
=> The 6th number is even
=> The 7th number is odd and so is the 8th number
Hence,the 3rd number and every third number after that are even.
So the numerical orders of the even numbers are divisible by 3
In the first 1000 numbers,there are :
(999  3) : 3 + 1 = 333 (even numbers) and :
1000  333 = 667 (odd numbers)

1 is odd,so the 3^{rd} number is even
=> The 4^{th} number is odd and so is the 5^{th} number
=> The 6^{th} number is even
=> The 7^{th} number is odd and so is the 8^{th} number
Hence,the 3^{rd} number and every third number after that are even.
So the numerical orders of the even numbers are divisible by 3
In the first 1000 numbers,there are :
(999  3) : 3 + 1 = 333 (even numbers) and :
1000  333 = 667 (odd numbers)

Thám Tử THCS Nguyễn Hiếu 27/03/2017 at 20:52
The odd number between the six remaining numbers is:
1337 : 7 = 191
So 7 consecutive numbers are 185 ; 187 ; 189 ; 191 ; 193 ; 195 ; 197
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Nễu Lả Ánh 28/03/2017 at 12:41
The odd number between the six remaining numbers is:
1337 : 7 = 191
So 7 consecutive numbers are 185 ; 187 ; 189 ; 191 ; 193 ; 195 ; 197

Pham Hoang Nam 18/04/2017 at 21:37
The odd number between the six remaining numbers is:
1337 : 7 = 191
So 7 consecutive numbers are 185 ; 187 ; 189 ; 191 ; 193 ; 195 ; 197

FA KAKALOTS 09/02/2018 at 22:06
We have :
22009 is even number
32009 = 34.502 . 3 = .....1 . 3 = ......3 (odd number)
72009 = 74.502 . 7 = .....1 . 7 = .....7(odd number)
= 94.502 . 9 = ......1 . 9 = .......9(odd number)
So : 22009 + 32009 + 72009 + 92009 = .....2 + .....3 + ....7 + .....9 = ......21 (odd number)

We have :
2^{2009} is even number
3^{2009} = 3^{4.502} . 3 = .....1 . 3 = ......3 (odd number)
7^{2009} = 7^{4.502} . 7 = .....1 . 7 = .....7(odd number)
= 9^{4.502} . 9 = ......1 . 9 = .......9(odd number)
So : 2^{2009} + 3^{2009} + 7^{2009} + 9^{2009} = .....2 + .....3 + ....7 + .....9 = ......21 (odd number)

Number One 02/04/2017 at 06:27We have :
22009 is even number
32009 = 34.502 . 3 = .....1 . 3 = ......3 (odd number)
72009 = 74.502 . 7 = .....1 . 7 = .....7(odd number)
= 94.502 . 9 = ......1 . 9 = .......9(odd number)
So : 22009 + 32009 + 72009 + 92009 = .....2 + .....3 + ....7 + .....9 = ......21 (odd number)
donald trump
27/03/2017 at 13:47

»ﻲ2004#ﻲ« 29/03/2017 at 06:10
We have : abcabc = abc x 1001 = abc x 7 x 11 x 13
Because abc is a prime number,the number of divisors of abcabc is :
(1 + 1)4 = 16

Indratreinpro 02/04/2017 at 22:12
Let a,b,c be the number of the correctly answered questions , unanswered questions , incorrectly answered questions of a participant respectively
Then the participant's total score is 5a + b  c with a + b + c = 30
If a is odd,then 5a and b + c are odd,so b  c is odd and 5a + b  c is even
If a is even,then 5a and b + c are even,so b  c is even and 5a + b  c is even
From 2 cases,we know that the total score of all participants is always an even number

Nếu bây giờ ngỏ ý . Liệu có còn kịp không 28/03/2017 at 12:29
Let a,b,c be the number of the correctly answered questions , unanswered questions , incorrectly answered questions of a participant respectively
Then the participant's total score is 5a + b  c with a + b + c = 30
If a is odd,then 5a and b + c are odd,so b  c is odd and 5a + b  c is even
If a is even,then 5a and b + c are even,so b  c is even and 5a + b  c is even
From 2 cases,we know that the total score of all participants is always an even number

Pham Hoang Nam 18/04/2017 at 21:39
It's 23,54

Vũ Việt Vương 01/04/2017 at 17:13
it's 23,54

FA KAKALOTS 09/02/2018 at 22:07
Let n is number of pages. I is the page which was removed.
1 + ... + n  i = 3030
3030 + i = ( n +1 ) * n : 2

Pham Hoang Nam 18/04/2017 at 21:41
Let n is number of pages. I is the page which was removed.
1 + ... + n  i = 3030
3030 + i = ( n +1 ) * n : 2

Nhat Lee 16/04/2017 at 17:33
Let n is number of pages. i is the page which was removed.
1+...+n i =3030
3030+i=(n+1) * n :2

If a is odd,then a^{3} and a^{2} are also odd,so a^{3} + a^{2} + 1 is odd
If a is even,then a^{3} and a^{2} are also even,so a^{3} + a^{2} + 1 is odd
So a^{3} + a^{2} + 1 is always odd with any integer a
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»ﻲ2004#ﻲ« 29/03/2017 at 06:11
If a is odd,then a3 and a2 are also odd,so a3 + a2 + 1 is odd
If a is even,then a3 and a2 are also even,so a3 + a2 + 1 is odd
So a3 + a2 + 1 is always odd with any integer a

Nếu bây giờ ngỏ ý . Liệu có còn kịp không 28/03/2017 at 12:31
If a is odd,then a3 and a2 are also odd,so a3 + a2 + 1 is odd
If a is even,then a3 and a2 are also even,so a3 + a2 + 1 is odd
So a3 + a2 + 1 is always odd with any integer a

Run my EDM 20/03/2017 at 12:22
Put \(\left(2k1\right)\left(2k+1\right)=123476543\)
\(\Leftrightarrow4k^21123476543=0\)
\(\Leftrightarrow4k^2123476544=0\)
\(\Leftrightarrow4\left(k^230869136\right)=0\)
\(\Leftrightarrow k^2=30869136=5556^2\)
\(\Leftrightarrow k=5556\)
\(\Rightarrow\left\{{}\begin{matrix}2k1=11111\\2k+1=11113\end{matrix}\right.\)
Ans : 11111 & 11113.
Donald Trump selected this answer. 
FA KAKALOTS 09/02/2018 at 22:08
Put (2k−1)(2k+1)=123476543
⇔4k2−1−123476543=0
⇔4k2−123476544=0
⇔4(k2−30869136)=0
⇔k2=30869136=55562
⇔k=5556
⇒{2k−1=111112k+1=11113
Ans : 11111 & 11113.

Nguyệt Nguyệt 20/03/2017 at 11:33
123476543 = 11111 x 11113

FA KAKALOTS 09/02/2018 at 22:08
a + b + c is odd ; 2b is even,so a + b + c  2b is odd
=> a  b + c is odd => (a + b + c)(a  b + c) is odd

a + b + c is odd ; 2b is even,so a + b + c  2b is odd
=> a  b + c is odd => (a + b + c)(a  b + c) is odd