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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.

Offline

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