Matches in DBpedia 2014 for { ?s ?p In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equationsatisfying x > y > 1 and n, m > 2 are (x, y, m, n) = (5, 2, 3, 5); and (x, y, m, n) = (90, 2, 3, 13).This may be expressed as saying that 31 and 8191 are the only two numbers that are repunits with at least 3 digits in two different bases.Balasubramanian and Shorey proved in 1980 that there are only finitely many possible solutions to the equations in (x,y,m,n) with prime divisors of x and y lying in a given finite set and that they may be effectively computed.. }
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- Goormaghtigh_conjecture abstract "In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equationsatisfying x > y > 1 and n, m > 2 are (x, y, m, n) = (5, 2, 3, 5); and (x, y, m, n) = (90, 2, 3, 13).This may be expressed as saying that 31 and 8191 are the only two numbers that are repunits with at least 3 digits in two different bases.Balasubramanian and Shorey proved in 1980 that there are only finitely many possible solutions to the equations in (x,y,m,n) with prime divisors of x and y lying in a given finite set and that they may be effectively computed.".