During my talk, I discuss various types of decompositions of 1 into a sum of egyptian fractions, i.e., the fractions with numerators being equal to 1.
I will focus on two main types of such decompositions. The first type is a decomposition where the prime factors of all denominators are fixed, whereas the second type is a decomposition where each denominator is a product of wo distinct primes. I will show some interesting results involving the minimal required number of fractions and minimal number of required primes.