Got it!!!
Thank you so much!!!
how can you be sure that after multiplying f and g, no coefficient will become zero. I understand that all terms will have different powers. But that does not stop a coefficient becoming 0 mod p.
How can a coeffiecient be 0?
For convinience lets say q=p-1.
See f is a polynomial with terms of multiple of power q,g is a polynomial with degree<q;
Lets say i is the power of a term in result,so i will be (j*q)+k where j denotes x^(jq) power if present in f,k denotes x^k power if present in g;
So as u can see ,i will always be distinct,so for each mul we get a distinct term,so for the coefficient to be 0,(a*b)modp should be 0(a is coefficient in f,b in g),which is not possible if a!=0,b!=0,p->prime
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oh sorry!! i get it now. This holds true because p is prime so, a*b mod p is never equal to 0. Thanks a lot!
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