MATH

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THE VALUE 2 TO THE 8TH POWER - 1 IS DIVISIBLE BY THREE PRIME NUMBERS. WHAT IS THE SUM OF THE THREE PRIME NUMBERS?

  • MATH -

    Just start at 2 and divide 255 which is (2^8)-1.

    255/2 =127.5

    Not divisible by 2.

    255/3 = 85

    We have one prime number, 3.

    255/5 = 51

    We have two prime numbers - 3,5.

    255/7 = 36.43

    Not divisible by 7

    255/9 = 28.33

    Not divisible by 9

    255/11 = 23.18

    Not divisible by 11

    .
    .
    .

    255/17 = 15

    We have three prime numbers - 3,5,17.

    So the sum of them are:

    3+5+17 = 25

  • MATH -

    or, since a^2-b^2 = (a-b)(a+b)
    (2^8-1) = (16-1)(16+1) = (4-1)(4+1)(16+1) = 3*5*17

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