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real number

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How many positive factors does
62x(63^3+63^2+63+1)+1 have?

(with solution pls... thanks...)

  • real number - ,

    63^3 + 63^2 + 63 + 1
    = 63^2(63 + 1) + (63+1)
    = (63^2 + 1)(63+1)
    = 3970 x 64

    62x(63^3+63^2+63+1)+1
    = 62 x 3970 x 64 + 1
    = 15752961
    = 2401x6561
    = 2401 x 3^8
    = 7x343x3^8
    = 7^4 x 3^8

    So now we need to take different combinations of factors, e.g. 7x7 x 3x3x3 would be a factor

    the four factors of 7 can be taken in 5 ways,
    that is, take none, take one, take 2, take 3 or take 4 of them
    in the same way, the eight 3's can be taken in 9 ways.
    So the total number of subsets of the above is
    5x9 or 45
    BUT, that would include taking neither the 7 nor the 3
    so we subtract 1

    number of positive factors is 44

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