Smallest integer such its n-th root,decimal root followed by 10 consecutive zeros

 
 
Determine the smallest possible positive integer P which is not a perfect n-th power, but in the decimal expansion of its n-th root, the decimal point is followed by at least ten consecutive zeroes.
 
 
n = 2

\sqrt {25000000000000000001} \; = \; 5 000000000. \overline{0000000000}99999...

 

n = 3

\sqrt[3]{ \,192459820704257 \,} \; = \; 57736.\overline{0000000000}9999662923...

 

n = 4

\sqrt[4]{ \,3400940858897 \,} \; = \; 1358.\overline{0000000000}9982531...

 

n = 5

\sqrt[5]{ \,428232184833 \,} \; = \; 212.\overline{0000000000}9901...

 

n = 6

\sqrt[6]{ \,117649000001 \,} \; = \; 70.\overline{0000000000}99165...

 

n = 7

\sqrt[7]{ \,52523350145 \,} \; = \; 34.\overline{0000000000}9247...

 

n = 8

\sqrt[8]{ \,25600000001 \,} \; = \; 20.\overline{0000000000}9765...

 

n = 9

\sqrt[9]{ \,20661046785 \,} \; = \; 14.\overline{0000000000}7528...

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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