Title: On the conjecture of Jeśmanowicz,
Abstract: We give a survey on some results covering the last 60 years concerning
Jeśmanowicz' conjecture. Moreover, we conclude the survey with a new result
by showing that the special Diophantine equation $$(20k)^x+(99k)^y=(101k)^z$$
has no solution other than $(x,y,z)=(2,2,2)$.