Determine the smallest possible positive integer P which is not a perfect tenth power, but in the decimal expansion of its tenth root, the decimal point is followed by at least 14 consecutive zeroes.
(In reply to
solution by Charlie)
My previous post purported to show the first 20 numbers fitting the puzzle description. However it neglected the possibility that an appropriate number might be higher than a perfect 10th power by more than one. The new version, below, shows the first 30 numbers meeting the criterion:
clc,clearvars
ct=0;
digits 50
for n=vpa(1):10000
n10=n^10+1;
root10=n10^(1/10);
while root10-floor(root10)<=1e-14
disp([n n10 root10])
ct=ct+1;
if ct>=30
break
end
n10=n10+1;
root10=n10^(1/10);
end
if ct>=30
break
end
end
P 10th root
[28.0, 296196766695425.0, 28.000000000000009453175438877110054825436961510186]
[29.0, 420707233300202.0, 29.000000000000006893154598867248365910275859328894]
[30.0, 590490000000001.0, 30.000000000000005080526342529082141548791447634585]
[31.0, 819628286980802.0, 31.000000000000003782202309560617690285029165615172]
[31.0, 819628286980803.0, 31.000000000000007564404619121231227489774653460096]
[32.0, 1125899906842625.0, 32.000000000000002842170943040399607524793552056139]
[32.0, 1125899906842626.0, 32.000000000000005684341886080796943130180067602113]
[32.0, 1125899906842627.0, 32.000000000000008526512829121192006816159546641755]
[33.0, 1531578985264450.0, 33.000000000000002154639121945256299826478777000175]
[33.0, 1531578985264451.0, 33.00000000000000430927824389051133352484505844889]
[33.0, 1531578985264452.0, 33.000000000000006463917365835765101095098844347717]
[33.0, 1531578985264453.0, 33.000000000000008618556487781017602537240134698226]
[34.0, 2064377754059777.0, 34.000000000000001646985389817153135334001684104289]
[34.0, 2064377754059778.0, 34.000000000000003293970779634305552637183708196019]
[34.0, 2064377754059779.0, 34.000000000000004940956169451457251909546072275851]
[34.0, 2064377754059780.0, 34.000000000000006587941559268608233151088776344445]
[34.0, 2064377754059781.0, 34.000000000000008234926949085758496361811820402463]
[34.0, 2064377754059782.0, 34.000000000000009881912338902908041541715204450565]
[35.0, 2758547353515626.0, 35.000000000000001268783729791490303401576012800083]
[35.0, 2758547353515627.0, 35.000000000000002537567459582980192851455544101765]
[35.0, 2758547353515628.0, 35.00000000000000380635118937446966834963859390533]
[35.0, 2758547353515629.0, 35.000000000000005075134919165958729896125162211064]
[35.0, 2758547353515630.0, 35.000000000000006343918648957447377490915249019251]
[35.0, 2758547353515631.0, 35.000000000000007612702378748935611134008854330177]
[35.0, 2758547353515632.0, 35.000000000000008881486108540423430825405978144127]
[36.0, 3656158440062977.0, 36.000000000000000984640042004851098746881329087681]
[36.0, 3656158440062978.0, 36.000000000000001969280084009701955114759578346695]
[36.0, 3656158440062979.0, 36.000000000000002953920126014552569103634747777167]
[36.0, 3656158440062980.0, 36.000000000000003938560168019402940713506837379223]
[36.0, 3656158440062981.0, 36.00000000000000492320021002425306994437584715299]
>>
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Posted by Charlie
on 2023-11-02 09:35:16 |
re: solution
