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## 'Powerful Factors' printed from http://nrich.maths.org/

Use the fact that:

$x^2-y^2$ |
= |
$(x-y)(x+y)$ |

$x^3+y^3$ |
= |
$(x+y)(x^2-xy+y^2)$ |

to find the highest power of $2$ and the highest power of $3$
which divide $5^{36}-1$.