39 lines
1.5 KiB
Plaintext
39 lines
1.5 KiB
Plaintext
Repunits are numbers that consist entirely of repetitions of the digit one (unity). The notation '''R<sub>n</sub>''' symbolizes the repunit made up of '''n''' ones.
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Every prime '''p''' larger than 5, evenly divides the repunit '''R<sub>p-1</sub>'''.
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;E.G.
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The repunit '''R<sub>6</sub>''' is evenly divisible by '''7'''.
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<span style=font-size:125%;font-weight:bold;padding-left:3em;>111111 / 7 = 15873</span>
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The repunit '''R<sub>42</sub>''' is evenly divisible by '''43'''.
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<span style=font-size:125%;font-weight:bold;padding-left:3em;>111111111111111111111111111111111111111111 / 43 = 2583979328165374677002583979328165374677</span>
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And so on.
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There are composite numbers that also have this same property. They are often referred to as ''deceptive non-primes'' or ''deceptive numbers''.
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The repunit '''R<sub>90</sub>''' is evenly divisible by the composite number '''91''' (=7*13).
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<div style=font-size:125%;font-weight:bold;padding-left:3em;>111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 / 91 = 1221001221001221001221001221001221001221001221001221001221001221001221001221001221001221</div>
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;Task
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* Find and show at least the first '''10 deceptive numbers'''; composite numbers '''n''' that evenly divide the repunit '''R<sub>n-1</sub>'''
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;See also
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;* [https://www.numbersaplenty.com/set/deceptive_number Numbers Aplenty - Deceptive numbers]
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;* [[oeis:A000864|OEIS:A000864 - Deceptive nonprimes: composite numbers k that divide the repunit R_{k-1}]]
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<br>
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