ON THE DIOPHANTINE EQUATION x 4 − q 4 = py 5

نویسنده

  • Diana Savin
چکیده

In this paper we study the Diophantine equation x4− q4 = py5, with the following conditions: p and q are different prime natural numbers, y is not divisible with p, p ≡ 3 (mod20), q ≡ 4 (mod5), p is a generator of the group (

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ON THE DIOPHANTINE EQUATION x 4 − q 4 = py 3

In this paper we study the Diophantine equation x4−q4 = py, with the following conditions: p and q are prime distincts natural numbers, x is not divisible with p, p ≡ 11 (mod12), q ≡ 1 (mod3), p is a generator of the group ( Zq , · ) , 2 is a cubic residue mod q.

متن کامل

ABOUT THE DIOPHANTINE EQUATION x 4 − q 4 = py r

In this paper, we prove a theorem about the integer solutions to the Diophantine equation x − q = py, extending previous work of K.Győry, and F.Luca and A.Togbe, and of the author. MSC (2000): 11D41

متن کامل

On Some Diophantine Equations (i)

In this paper we study the equation m−n = py,where p is a prime natural number, p≥ 3. Using the above result, we study the equations x + 6pxy + py = z and the equations ck(x 4 + 6pxy + py) + 4pdk(x y + pxy) = z, where the prime number p ∈ {3, 7, 11, 19} and (ck, dk) is a solution of the Pell equation, either of the form c −pd = 1 or of the form c − pd = −1. I. Preliminaries. We recall some nece...

متن کامل

On Some Diophantine Equations (ii)

In [7] we have studied the equation m − n = py, where p is a prime natural number p ≥ 3. Using the above result, in this paper, we study the equations ck(x 4 + 6px y +py) + 4pdk(x y + pxy) = 32z with p ∈ {5, 13, 29, 37}, where (ck, dk) is a solution of the Pell equation ∣∣c2 − pd2∣∣ = 1.

متن کامل

The Diophantine Equation 8x + py = z2

Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ± 3(mod  8), then the equation 8 (x) + p (y) = z (2) has no positive integer solutions (x, y, z); (ii) if p ≡ 7(mod  8), then the equation has only the solutions (p, x, y, z) = (2 (q) - 1, (1/3)(q + 2), 2, 2 (q) + 1), where q is an odd prime with q ≡ 1(mod  3); (iii) if p ≡ 1(mod  8)...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009