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Bill gates

20/03/2017 at 10:48
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It is given 7m +n = mn +11 = prime, where m and n are both prime too.

Find \(m^2+n^2\).


Prime Numbers and Composite Numbers

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  • ...
    ¤« 24/02/2018 at 13:57

    We have : 7m + n = mn + 11

    => 7m + n - mn = 11

    => m(7 - n) - 7 + n = 4

    => (m - 1)(7 - n) = 4

    So we have a table as shown :

    m - 1 1 2 4
    7 - n 4 2 1
    m 2 3 5
    n 3 5 6 (absurd)
    7m + n 17 26 (absurd) x

    Hence,we have m = 2 ; n = 3 and m2 + n2 = 13

  • ...
    Phan Thanh Tinh Coordinator 28/03/2017 at 19:51

    We have : 7m + n = mn + 11

    => 7m + n - mn = 11

    => m(7 - n) - 7 + n = 4

    => (m - 1)(7 - n) = 4

    So we have a table as shown :

    m - 1 1 2 4
    7 - n 4 2 1
    m 2 3 5
    n 3 5 6 (absurd)
    7m + n 17 26 (absurd) x

    Hence,we have m = 2 ; n = 3 and m2 + n2 = 13

     



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