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| 600 sixes (Posted on 2019-02-11) |
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Can a number consisting of 600 sixes and some zeros be a square?
Proving that a natural number made entirely of 6's and 0's is not a square.
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 | Comment 2 of 3 | 
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The term "infinite descent" should not be used here. If you were stripping off terminal <nobr aria-hidden="true" style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">0</nobr><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>'s two at a time, the term would be technically right. But you are stripping off all the terminal <nobr aria-hidden="true" style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">0</nobr><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>'s to get <nobr aria-hidden="true" style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">N′</nobr><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>N</mi><mo>′</mo></msup></math>, so you are reaching the square <nobr aria-hidden="true" style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">N′</nobr><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>N</mi><mo>′</mo></msup></math> that ends in a <nobr aria-hidden="true" style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">6</nobr><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> in one step. Apart from that inaccuracy of wording, the proof is good. Update Madalin Stunt Cars 2 full version.
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