- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,638

Determine $d-b$.

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,638

Determine $d-b$.

- Mar 31, 2013

- 1,295

Determine $d-b$.

Further as $a^5=b^4$ so there exists y such that $a=y^4$ and $b=y^5$

Now

c-a=19

$=> x^2-y^4=19$

$=> (x-y^2)(x+y^2)=19$

As 19 is prime and $x+y^2 > x- y^2$ we have

$x-y^2=1$ and $x+y^2=19$

Solving these we get $x=10$ and $y = 3$

So $d-b = 10^3 - 3^5 = 1000 - 243= 757$