Currently displaying 1 – 20 of 21

Showing per page

Order by Relevance | Title | Year of publication

On blocks of arithmetic progressions with equal products

N. Saradha — 1997

Journal de théorie des nombres de Bordeaux

Let f ( X ) [ X ] be a monic polynomial which is a power of a polynomial g ( X ) [ X ] of degree μ 2 and having simple real roots. For given positive integers d 1 , d 2 , , m with < m and gcd ( , m ) = 1 with μ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) f ( x + ( k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) 0 for 0 j < k has only finitely many solutions in integers x , y and k 1 except in the case m = μ = 2 , = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .

Page 1 Next

Download Results (CSV)