On the diophantine equation x(x-1)...(x-(m-1 ) )= λy(y-1 )...(y-(n-1 ) )+ l
نویسندگان
چکیده
منابع مشابه
On the Diophantine equation q n − 1 q − 1 = y
There exist many results about the Diophantine equation (qn − 1)/(q − 1) = ym, where m ≥ 2 and n ≥ 3. In this paper, we suppose that m = 1, n is an odd integer and q a power of a prime number. Also let y be an integer such that the number of prime divisors of y − 1 is less than or equal to 3. Then we solve completely the Diophantine equation (qn − 1)/(q − 1) = y for infinitely many values of y....
متن کاملON THE DIOPHANTINE EQUATION x m − 1 x − 1 = yn − 1 y − 1
There is no restriction in assuming that y > x in (1) and thus we have m > n. This equation asks for integers having all their digits equal to one with respect to two distinct bases and we still do not know whether or not it has finitely many solutions. Even if we fix one of the four variables, it remains an open question to prove that (1) has finitely many solutions. However, when either the b...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa110-4-3