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download PDF Abstract: For given integers a,b, and j at least 1 we determine the set of integers nfor which a^n-b^n is divisible by n^j. For j=1,2, this set is usually infinite;we find explicitly the exceptional cases for which a,b the set is finite. Forj=2, we use Zsigmondy"s Theorem for this. For j at least 3 & gcd(a,b)=1, theset is probably always finite; this seems difficult to prove, however.We also show that determination of the set of integers n for which a^n+b^n isdivisible by n^j can be reduced khổng lồ that of the above set.
Subjects: Number Theory (math.NT)
MSC classes: 11B37; 11D61
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