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Determine with proof all triples (a, b, ...

Determine with proof all triples (a, b, c) of positive integers satisfying `1/a+2/b+3/c=1` where a is a prime number and `a le b le c`

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The correct Answer is:
(2,5,30)(2,6,18)(2,7,14)(2,8,12)(2,10,10)(3,4,6)(3,6,9)
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Knowledge Check

  • The number of positive integer solutions of a+b+c=60, where a is a factor of b and c, is

    A
    184
    B
    200
    C
    144
    D
    270

  • How many positive integral solutions exist for : ab+cd = a+b+c+d, where 1 le a le b le c le d ?

    A
    (A) 0
    B
    (B) 2
    C
    (C) 3
    D
    (D) none of these

  • The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

    A
    `240`
    B
    `480`
    C
    `960`
    D
    none of these

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    The number of triplets (a,b,c) of positive integers satisfying the equation |(a^3 + 1, a^2b, a^2c),(ab^2, b^3 + 1, b^2c),(ac^2, bc^2, c^3+1)| = 11 is/are :

    If a, b and c are positive integers such that (1)/(a+(1)/(b+(1)/(c+(1)/(2))))=(16)/(23) then what is the mean of a,b and c?

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