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    Hello, I am having trouble obtaining an answer for this question. All help is appreciated I have already acquired all the correct working out through my own endeavour but I am struggling to obtain the solution.



    The answer being:


    Can someone also please explain what the question means by "the number of pairs of positive integers"

    Thanks again, please help if possible
    (I have resposted this in the Math forum in order to gain a response, sorry if this is not allowed)
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    (Original post by mubmoh)
    Can someone also please explain what the question means by "the number of pairs of positive integers"
    We have pairs of positive integers, e.g. (1,2), (1,4), (5,33), and that is three pairs of positive integers.

    In your question each solution to the equation is a pair of positive integers, (x,y). One solution is (2^9,2^8) i.e. x=2^9 and y=2^8. How many such pairs are there?
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    (Original post by ghostwalker)
    We have pairs of positive integers, e.g. (1,2), (1,4), (5,33), and that is three pairs of positive integers.

    In your question each solution to the equation is a pair of positive integers, (x,y). One solution is (2^9,2^8) i.e. x=2^9 and y=2^8. How many such pairs are there?
    Thanks for the help, I've figured it out now :P But quick question am I right in assuming (2,4) is different than (4,2)

    1st Solution: (2^{10} - 2) + 2(1) = 2^{10}

2nd Solution: (2^{10} - 4) + 2(2) = 2^{10}

3rd Solution: (2^{10} - 6) + 2(3) = 2^{10}

...

(2^{9} - 2)th Solution: (4) + 2(2^{9} - 2) = 2^{10}

(2^{9} - 1)th Solution: (2) + 2(2^{9} -1) = 2^{10} 

Therefore there are (2^{9} - 1) possible pairs of solutions

    I'm not that good at using Latex, sorry for any inconvenience
    I would rep but it's telling me to rep other people first
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    (Original post by mubmoh)
    Thanks for the help, I've figured it out now :P But quick question am I right in assuming (2,4) is different than (4,2)
    Yes, they're different.

    In this case the first value refers to x, and the second to y.

    In general, values written in parentheses are ordered, e.g. coordinates.
 
 
 
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