A045616 - OEIS

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A045616

Primes p such that 10^(p-1) == 1 (mod p^2).

3, 487, 56598313 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`Primes p such that the decimal fraction 1/p has same period length as 1/p^2.` `No further terms below 3.4*10^13 (cf. Fischer's table)`
	REFERENCES	`J. Brillhart, J. Tonascia, and P. Weinberger, On the Fermat quotient, pp. 213-222 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.` `Richard K. Guy, Unsolved Problems in Number Theory, Springer, 2004, A3.` `Peter L. Montgomery, New Solutions of a^(p-1) = 1 (mod p^2), Math. Comp. 61 (1993), 361-363.` `Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28.`
	LINKS	`Table of n, a(n) for n=1..3.` `Helmut Richter, The period length of the decimal expansion of a fraction` `Helmut Richter, The Prime Factors Of 10^486-1` `Richard Fischer, Fermat quotients B^(P-1) == 1 (mod P^2)`
	CROSSREFS	`Cf. A001220, A014127, A123692, A123693, A111027, A039951.` `Sequence in context: A140015 A203681 A195611 * A198705 A198624 A198652` `Adjacent sequences: A045613 A045614 A045615 * A045617 A045618 A045619`
	KEYWORD	`bref,hard,nonn,nice,more`
	AUTHOR	`Helmut Richter (richter(AT)lrz.de)`
	EXTENSIONS	`56598313 was announced in the paper by Brillhart et al. - Helmut Richter (richter(AT)lrz.de), May 17 2004`
	STATUS	`approved`

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Last modified December 13 15:21 EST 2013. Contains 233297 sequences.