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Solve

Posted on: January 23rd, 2014 by
1

Solve for integers x, y: 19x^3-84y^2=1984.

- via Russian Math Olympiad practice problems


One Response to Solve

  1. Sudharsan had this to say about that:

    No solutions possible for x & y.

    Take Modulo 7 either side:

    5x^3 = 3.

    Check this table
    x x^3 5x^3 Mod(7)
    1 1 5 5
    2 8 40 5
    3 27 135 2
    4 64 320 5
    5 125 625 2
    6 216 1080 2

    Neither corresponds to 3..

    Same case when mod(19) is operated.
    Hence there is no REAL SOLUTION possible.

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