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What is the largest integer n such that 1440/(n^2-1) is an integer?

  • math -

    factors of 1440
    2x720
    3x480
    4x360
    5x288
    6x240
    8x180
    9x160
    10x144
    12x120
    15x96
    16x90
    18x80
    20x72
    24x60
    30x48
    32x45
    36x40 ---> that's all of them

    values of n^2-1
    1,3,8,15,24,35,48,63,80,99,120,143,168,195,288,325,360,399,440,483,529,575,624,675,728

    the largest of these that show up in the factor list is 360
    and 360 = 19^2 - 1 , where n = 19

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