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On blocks of arithmetic progressions with equal products

N. Saradha — 1997

Journal de théorie des nombres de Bordeaux

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

On perfect powers in products with terms from arithmetic progressions

N. Saradha — 1997

Acta Arithmetica

Transcendence measure for η/ω

N. Saradha — 2000

Acta Arithmetica

Squares in products with terms in an arithmetic progression

N. Saradha — 1998

Acta Arithmetica

Application of the explicit abc-conjecture to two Diophantine equations

N. Saradha — 2012

Acta Arithmetica

On a problem of Pillai and its generalizations

L. Hajdu; N. Saradha — 2010

Acta Arithmetica

Number of solutions of cubic Thue inequalities with positive discriminant

N. Saradha; Divyum Sharma — 2015

Acta Arithmetica

Let F(X,Y) be an irreducible binary cubic form with integer coefficients and positive discriminant D. Let k be a positive integer satisfying $k < ({(3 D)}^{1 / 4}) / 2 π$ . We give improved upper bounds for the number of primitive solutions of the Thue inequality $| F (X, Y) | \leq k$ .

Arithmetic progressions with common difference divisible by small primes

N. Saradha; R. Tijdeman — 2008

Acta Arithmetica

On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2

N. Saradha; T.N. Shorey; R. Tijdeman — 1995

Acta Arithmetica

On a conjecture of Pomerance

L. Hajdu; N. Saradha; R. Tijdeman — 2012

Acta Arithmetica

Almost perfect powers in arithmetic progression

N. Saradha; T. N. Shorey — 2001

Acta Arithmetica

On the irreducibility of certain polynomials with coefficients as products of terms in an arithmetic progression

Carrie E. Finch; N. Saradha — 2010

Acta Arithmetica

On the equation $n (n + d) \dots (n + (i ₀ - 1) d) (n + (i ₀ + 1) d) \dots (n + (k - 1) d) = y^{l}$ with 0 < i₀ < k-1

N. Saradha; T. N. Shorey — 2007

Acta Arithmetica

Transcendental values of the p-adic digamma function

M. Ram Murty; N. Saradha — 2008

Acta Arithmetica

Some infinite products with interesting continued fraction expansions

C. G. Pinner; A. J. Van der Poorten; N. Saradha — 1993

Journal de théorie des nombres de Bordeaux

We display several infinite products with interesting continued fraction expansions. Specifically, for various small values of $k$ necessarily excluding $k = 3$ since that case cannot occur, we display infinite products in the field of formal power series whose truncations yield their every $k$ -th convergent.