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.
clc,clearvars
ct=0;
digits 50
for n=vpa(1):10000
n10=n^10+1;
root10=n10^(1/10);
if root10-floor(root10)<=1e-14
disp([n n10 root10])
ct=ct+1;
if ct>=20
break
end
end
end
finds the first 20 such, the first of which is 296196766695425:
floor
of 10th
root P 10th root of P
[28.0, 296196766695425.0, 28.000000000000009453175438877110054825436961510186]
[29.0, 420707233300202.0, 29.000000000000006893154598867248365910275859328894]
[30.0, 590490000000001.0, 30.000000000000005080526342529082141548791447634585]
[31.0, 819628286980802.0, 31.000000000000003782202309560617690285029165615172]
[32.0, 1125899906842625.0, 32.000000000000002842170943040399607524793552056139]
[33.0, 1531578985264450.0, 33.000000000000002154639121945256299826478777000175]
[34.0, 2064377754059777.0, 34.000000000000001646985389817153135334001684104289]
[35.0, 2758547353515626.0, 35.000000000000001268783729791490303401576012800083]
[36.0, 3656158440062977.0, 36.000000000000000984640042004851098746881329087681]
[37.0, 4808584372417850.0, 37.000000000000000769457227624679956564668274832434]
[38.0, 6278211847988225.0, 38.000000000000000605267883914695094282271133679891]
[39.0, 8140406085191602.0, 39.00000000000000047909157837894340855844488173986]
[40.0, 10485760000000001.0, 40.000000000000000381469726562499983629095368087293]
[41.0, 13422659310152402.0, 41.000000000000000305453629214809328569623115678443]
[42.0, 17080198121677825.0, 42.00000000000000024589878700935261768089876227873]
[43.0, 21611482313284250.0, 43.000000000000000198968304795865640666771362587126]
[44.0, 27197360938418177.0, 44.000000000000000161780402516359296830689352758512]
[45.0, 34050628916015626.0, 45.000000000000000132156149335715693971364832491179]
[46.0, 42420747482776577.0, 46.000000000000000108437504592951009887543013891808]
[47.0, 52599132235830050.0, 47.000000000000000089355086295480799575318956301921]
>>
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Posted by Charlie
on 2023-11-02 08:56:23 |
solution
