Diophantine equations involving normalized binomial mid-coefficients

作者：Yang Shichun^*; Togbe Alain; Wu Wenquan

来源：Publicationes Mathematicae-Debrecen, 2013, 83(3): 415-433.

DOI：10.5486/PMD.2013.5541

• normalized binomial mid-coefficients
• Diophantine equations
• power means
• p-adic valuation

For a positive integer n, let mu(n) be the normalized binomial mid-co-efficients. We discuss the following Diophantine equation involving power means of n variables mu(i).
M-k(mu(a1),...,mu(an)) = M-l(mu(b1),...,mu(bn)), k, l is an element of Z.
For n = 2,3 and other general cases, we get some results on this equation. Moreover, for k = l = 0 and for every n >= 3, we obtain infinitely many solutions of equation mu(a1)mu(a2)...mu(an) = mu(b1)mu(b2)...mu(bn).

• 出版日期2013-10
• 单位伊犁师范大学; 南宁师范大学