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    Find all integers x and y which satisfy the equation
    x² - 3y² = 17

    taken from
    http://www.ucc.ie/mathsoc/pastpapers/s1987.shtml

    I cannot figure out how to start. Never dealt with anything of this type before.
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    Try to solve it mod 3.
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    Google Pell equations and continued fractions.
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    (Original post by Mr M)
    Google Pell equations and continued fractions.
    Thanks
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    (Original post by Mr M)
    Google Pell equations and continued fractions.
    Unless I'm mistaken, that's not the best advice here.
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    (Original post by DFranklin)
    Unless I'm mistaken, that's not the best advice here.
    He said he had never dealt with equations of this type so I was trying to help him research the topic further. I had already seen your post.

    Message to mrmanps: In matters such as this, it is probably best to listen to DF first and me second.
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    (Original post by DFranklin)
    Try to solve it mod 3.
    Is there a good website you could point me to in order to recap this? It's been a while
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    http://en.wikipedia.org/wiki/Modular_arithmetic ?

    (In this particular case, reducing mod 3 eliminates y, and you can then use trial and error to find all possible solutions in x).
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    (Original post by DFranklin)
    http://en.wikipedia.org/wiki/Modular_arithmetic ?

    (In this particular case, reducing mod 3 eliminates y, and you can then use trial and error to find all possible solutions in x).
    so it becomes x²=2?
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    (Original post by mrmanps)
    so it becomes x²=2?
    x^2 = 2 mod 3, yeah.
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    (Original post by around)
    x^2 = 2 mod 3, yeah.
    so how am i suppose to find an integer vale of x now?
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    (Original post by mrmanps)
    so how am i suppose to find an integer vale of x now?
    Are you certain there are integer solutions to find?
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    (Original post by Mr M)
    Are you certain there are integer solutions to find?
    Q10 from this past paper
    taken from
    http://www.ucc.ie/mathsoc/pastpapers/s1987.shtml
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    Maybe substituting x=3n+2 would help? It may not though, just an idea.
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    (Original post by james22)
    Maybe substituting x=3n+2 would help? It may not though, just an idea.
    reduces to 9n²+12n+2=0 which doesn't have integer roots
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    (Original post by mrmanps)
    ...
    Can you prove there are no square numbers that leave a remainder of 2 after division by 3?
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    I've just managed to deduce that there are no integer solutions. though my method is a bit rough and probobly has a few errors in it.

    I used the fact that x^2 must be of the form 3n+2, then made that substitution into the original equation, solved it for n and showed that there is no integer n which makes y an integer. It involved showing that 3y^2+19 colud never be a square which was the hardest part.
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    (Original post by james22)
    I've just managed to deduce that there are no integer solutions. though my method is a bit rough and probobly has a few errors in it.

    I used the fact that x^2 must be of the form 3n+2, then made that substitution into the original equation, solved it for n and showed that there is no integer n which makes y an integer. It involved showing that 3y^2+19 colud never be a square which was the hardest part.
    So this question (taken from an exam paper) see the first thread, is not possible to find a pair of integer solutions for? odd
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    (Original post by mrmanps)
    So this question (taken from an exam paper) see the first thread, is not possible to find a pair of integer solutions for? odd
    Well a solution can be that there are no solutions.
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    (Original post by Mr M)
    Well a solution can be that there are no solutions.
    True.
 
 
 
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