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Math

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Is 4^33 + 3^44 divisible by 5?
Please help ASAP. This is due tomorrow. Thank you very much :)

  • Math -

    yes

    look at powers of 4
    4^1 = 4
    4^2 = 16
    4^3 = 64
    4^4 =256
    ....
    every even indexed power ends in 6, every odd indexed power ends in 4
    so 4^33 ends in 4

    now look at the powers of 3
    3^1 = 3
    3^2 = 9
    3^3 = 27
    3^4 = 81
    3^5 = 243
    3^6 = 729
    ...
    the answers end in 3 9 7 1 3 9 7 1 ...
    even exponents end in either 9 or 1
    if the even exponent is also a multiple of 4, the answer ends in a 1
    so 3^44 will end with a 1

    so if we add a number ending in 4 to a number ending in 1
    we get a number ending in 5 which is divisible by 5

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