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...The method of vieta jumping yimin ge sometimes called root ipping is a for solving type number theory problems this has been used extensively in mathematicalcompetitions mostrecentlyattheinternationalmathematical olympiad inthisarticle we analyze and present some its application can be very useful involving divis ibility positive integers idea to assume existence solution which statement question wrong then consider given relation as quadratic equation one variables using s formula display second next step show that new valid smaller than previous by argument innite descent or assuming minimality rst get contradiction illustrate how works let us solve three classical problem considered historical it was submitted imo west germany arthur engel wrote following note about diculty nobody six members australian committee could two were georges szekeres his wife both famous solvers posers because sent four most renowned theorists they asked work on hours none them time jury th marked with do...