Yes, the chromosome number of zygote, embryonal cell and adult of a particular organism is always constant.Meiosis is the cell division which happens during gametogenesis,. This results in number of chromosomes getting halved in gametes. When fertilization happens, the number of chromosomes becomes equal to that in somatic cells. After that, mitosis takes place during rest of the stages of life. So, the constancy of chromosomal number is maintained in all the three stages.