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#1 2016-07-22 22:47:05
- Srikantan
- Member
- From: Tanjore
- Registered: 2016-06-04
- Posts: 42
Find integers
Find integers x and y such that
2(x^4) + 1987 = 3(y^4)
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#2 2016-07-23 01:09:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Find integers
Hi;
There are none.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2016-07-23 01:31:17
- Srikantan
- Member
- From: Tanjore
- Registered: 2016-06-04
- Posts: 42
Re: Find integers
Ok any logic behind the answer please
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#4 2016-07-23 01:47:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Find integers
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2016-07-23 02:05:25
- Srikantan
- Member
- From: Tanjore
- Registered: 2016-06-04
- Posts: 42
Re: Find integers
Sorry can you explain in detail pls. I m just in school
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#6 2016-07-23 02:12:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Find integers
Have you learned about modulo yet?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2016-07-23 02:13:27
- Srikantan
- Member
- From: Tanjore
- Registered: 2016-06-04
- Posts: 42
Re: Find integers
I have but not sure how to apply here
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#8 2016-07-23 02:18:11
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Find integers
Take the integers 0 ,1,2,3,4 and plug them into y one at a time in
and tell me what you get.
Then plug those same integers into x one at a time in
and tell me what you get.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2016-07-23 02:43:33
- thickhead
- Member
- Registered: 2016-04-16
- Posts: 1,086
Re: Find integers
Yes. bobbym is right.Broadly speaking, if the given relation were to hold good,y has to be odd, x can either be odd or even. So y^4 will end with 1 and 3y^4 will end with 3.( Even integer)^4 can only end with 6 So 2 x^4 will only end with 2 whether x is odd or even. So the difference 3y^4-2x^4 should end with 1. but in the problem given it ends with 7 (1987). So the relation can not be satisfied.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#10 2016-07-23 03:14:44
- Srikantan
- Member
- From: Tanjore
- Registered: 2016-06-04
- Posts: 42
Re: Find integers
If y is 5 then y^4 will end with 5 right
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#11 2016-07-23 04:31:45
- thickhead
- Member
- Registered: 2016-04-16
- Posts: 1,086
Re: Find integers
Yes I had left out the exception 5.Here 3y^5 will end with 5 subtract 1987 and you will get a number ending with 8 which is not a valid ending for 2 x^4. If it is -1987 there is some possibility to be investigated.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#12 2016-07-23 05:42:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Find integers
Hi Srikantan;
You did not answer the two questions I gave you.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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