This question was asked in complex analysis end term of previous year and I am trying to solve it to gain some experience.
I need help with following question:
If f and g are entire functions with no common zeroes and if h is an entire function show that h can be always written as h=fF+gG.with some entire functions F and G.
I am completely stumped on which theorem should I use to solve it as this question seems very hard for me and I am unable to get any intuition. Also, not much assignments were given to us by course instructor due to Covid-19 and so it's a problem as I am often blank on how to approach some questions.
Entire functions are functions which are holomorohic on all of $\mathbb{C} $ .
Kindly shed some light on solution of this problem.