Modular congruences
If there exists a polynomial with two zeros and , then is never divisible by:
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1 solution
by observation we get that a+b = 6 and ab=1 .... we establish the relationship (using symmetric polynomials) : - s= a^n+b^n = 6(a^n-1+b^n-1)- (a^n-2 +b^n-2) ...... we find s is congruent to (a^n-1+b^n-1) + (a^n-2+b^n-2) (modulo 5) ...... considering this sequence of modular congruencies we find it is periodic and never divisible by 5