Toward the goal of using technology in mathematical exploring and teaching, examples on executing Euclidean algorithm and on finding the intersections of exponential functions and logarithm functions based on various bases respectively will be illustrated in this paper. taking advantage of nowadays modern technology to overcome the tedious calculation within the Euclidean algorithm is a crucial task. based on the essence of ancient Chinese "Chinese" Dayan qiuyshishu of qin jiushao , we explore integers solutions of ax + by =1 in a systematic way in excel spread sheet for relative primes a and b. moreover, a table together with a simple formula is introduced to keep records of all iterations in a sequence of calculations. in term of GSP, it is easy to realize that the number of intersections of the expontial function y = a and the logarithm function y = y log lepends on the value of the base a; and we found unexpectedly that there are three intersections under some values of a. we then determine analytically that these two functions have there intersections if and only if a lies in the ope interval (0,e). all dynamic environments are available in a CD-ROM on request.