# Unknown powers 2

Number Theory Level 4

Let a, b and c be three positive integers so that

$$a+b+c=19\\ \\ { a }^{ b }+{ b }^{ c }+{ c }^{ a }=1149201$$

Let

$$\frac { 1 }{ a } +\frac { 1 }{ b } +\frac { 1 }{ c } =\frac { x }{ y }$$

where x and y are positive coprime integers.

Find the value of x+y.

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