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A130058
Numbers m such that k = m*23^2 divides 3^(k-1) - 2^(k-1).
6
1, 67, 89, 133, 199, 331, 617, 793, 881, 5281, 8911, 11419, 13333, 22177, 23585, 26467, 35113, 35839, 38897, 40657, 44023, 54913, 65869, 67849, 70819, 92929, 105469, 107185, 114247, 124279, 144673, 153253, 159259, 185329, 196945, 225589
OFFSET
1,2
COMMENTS
All prime p>3 divide 3^(p-1) - 2^(p-1). It appears that 1 and 529 = 23^2 are the only perfect squares in A073631. Most terms of A073631 are squarefree. First 50 nonsquarefree terms of A073631 are the multiples of 23^2.
Conjecture: All nonsquarefree terms of A073631 are the multiples of 23^2.
Prime terms are listed in A130059. Note that the many terms (namely, 1, 133, 793, 8911, 13333, 22177, 26467, 38897, 44023, 54913, 65869, ...) also belong to A073631.
MATHEMATICA
Do[ k=n*23^2; f=PowerMod[ 3, k-1, k ] - PowerMod[ 2, k-1, k ]; If[ IntegerQ[ f/k ], Print[ n ] ], {n, 1, 1000000} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 04 2007
STATUS
approved