Markoff numbers and ambiguous classes
نویسندگان
چکیده
منابع مشابه
Markoff numbers and ambiguous classes
The Markoff conjecture states that given a positive integer c, there is at most one triple (a, b, c) of positive integers with a ≤ b ≤ c that satisfies the equation a2 + b2 + c2 = 3abc. The conjecture is known to be true when c is a prime power or two times a prime power. We present an elementary proof of this result. We also show that if in the class group of forms of discriminant d = 9c2 − 4,...
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By making use of only simple facts about congruence, we first show that every even Markoff number is congruent to 2 modulo 32, and then establish the uniqueness for those Markoff numbers c where one of 3c − 2 and 3c + 2 is a prime power, 4 times a prime power, or 8 times a prime power.
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2009
ISSN: 1246-7405
DOI: 10.5802/jtnb.701