p-adic Continued Fractions Ⅲ

1.Introduction In order to discuss the irrationality, the transcendence and the algebraic independence for p-adic numbers, the first author introduced in two previous papers [1, 2] a simple form for p-adic continued fraction which is called p-adic simple continued fraction by making use of the algebraic theory of continued fraction in the real field mentioned by Schmidt, and gave a sufficient condition for certain p-adic integers which and whose sum, defference, product and quotient are all p-adic transcendental numbers.