MathDB

A positive integer

n

is called egyptian if there exists a strictly increasing sequence

0<a_1<a_2<\dots<a_k=n

of integers with last term

n

such that

\frac{1}{a_1}+\frac{1}{a_2}+\dots+\frac{1}{a_k}=1.

(a) Determine if

n=72

is egyptian. (b) Determine if

n=71

is egyptian. (c) Determine if

n=72^{71}

is egyptian.

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