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A125775
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Numbers n such that 5^n (mod n) = 5^n (mod n^2).
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3
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1, 2, 4, 5, 6, 12, 25, 42, 52, 84, 125, 156, 186, 372, 625, 1092, 1218, 1302, 1806, 2436, 2604, 2756, 3125, 3612, 4836, 5334, 7212, 8268, 10668, 12324, 15625, 15918, 18858, 19140, 20771, 24492, 26080, 31668, 31836, 33852, 37716, 37758, 40487, 41542
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) includes all powers of 5. a(2) = 2, a(4) = 5, a(35) = 20771 and a(43) = 40487 are the only listed primes in a(n). There are more known primes in a(n) that are listed in A123692(n) = {2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801, ...} Primes p such that p^2 divides 5^(p-1) - 1.
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MATHEMATICA
| Do[f=PowerMod[5, n, n]; g=PowerMod[5, n, n^2]; If[f==g, Print[n]], {n, 1, 1000000}]
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CROSSREFS
| Cf. A123692 = Primes p such that p^2 divides 5^(p-1) - 1. Cf. A068535 = numbers n such that 2^n (mod n) = 2^n (mod n^2). Cf. A125773 = numbers n, that are not the powers of 2, such that 2^n (mod n) = 2^n (mod n^2). Cf. A125774 = numbers n such that 3^n (mod n) = 3^n (mod n^2).
Sequence in context: A194600 A006539 A031150 * A191165 A058637 A026473
Adjacent sequences: A125772 A125773 A125774 * A125776 A125777 A125778
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 07 2006
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