On The Linear Independence Measures Of 1,log(1-1/a),log(1+1/a)

Let α∈R/Q,If for any κ>0,there exists q≥q0(ε),such that |α-p/q|≥q-μ-ε, for all integers p and q with q≥q0(ε),then the real unmber μ≥0 is said to be an irrationality measure of α.The minimum of those number μ is denoted by μ(α).Let α0,α1,…,αn be real numbers linearly independent over Q,If for any ε>0,there exists q≥q0(ε),such that |pα0+q1α1+…+qnαn|≥H-v-ε, for all integers p and qi with H=max(|q1|,|q2|,…,|qn|)≥H0(ε),then the minimun of those u is denoted by u(α0,α1,…,αn).Let α∈Z and α≥2,in this paper:we mainly discussed the linear independence measure of 1,log(1-1/a),log(1+1/a).We have the better linear independence measures than the last one for a=((2m-1)3k+1)/2 and for a=((2m-1)3k-1)/2 with m,k∈Z+.In this work,we also discuss the Diophantine equation x2+4n=y11 and give its all the integer solutions for n=6,7.