# Rationalisation......sounds easy

Number Theory Level 5

$\large \frac{1}{ \sqrt[7]{531441} + \sqrt[7]{472392} + \sqrt[7]{419904} + \sqrt[7]{373248} + \sqrt[7]{331776} + \sqrt[7]{294912} + \sqrt[7]{262144} }$

After rationalizing the denominator of the above number. It appears in the form $$\large \frac{ \sqrt[7]{a} - \sqrt[7]{b} + \sqrt[7]{c} }{d}$$

Find $$a - b + c + d$$ .

Note - $$a > b$$ , gcd(a,b,c,d) = 1 .

This problem is a part of the sets - 3's & 4's & " N " for number theory

Follw me for more questions in the future.

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