February 27th, 2018, 03:46 AM  #1 
Member Joined: Sep 2014 From: Morocco Posts: 43 Thanks: 0  Proof by induction
Hello, I found this interesting result and I wanted to demonstrate it through induction: https://ibb.co/fdYjfx where the sigmas are symmetric functions (it's described in the picture, and apologies for it being in French). The result is true for each x1, x2, ..., xn in the sets of the reals or of the complex numbers. For n = 1, no issue arises, however it is the next step which appears quite tricky to me. I tried to use the induction hypothesis by splitting the product, but to no avail. Could I have some ideas? Best regards. (Apologies if this is the wrong board) 
February 27th, 2018, 01:09 PM  #3 
Member Joined: Sep 2014 From: Morocco Posts: 43 Thanks: 0 
Thanks skipjack, do you  by any chance  have an idea for induction?


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