# Perfect Cube, Fourth Powers, Fifth Powers, Sixth Powers!

Number Theory Level 4

For natural numbers $$a,b,c,d$$, we are given

$\begin{eqnarray} a^5 & = & b^6 \\ c^3 & = & d^4 \\ d-a & = & 61 \\ \end{eqnarray}$

What is the value of $$c-b$$?

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