Number theory · Primality · Algebraic factorisation · Difference of squares · Powers of three · Compositeness proofs
(a) Factor the expression \(x^{4}+x^{2}y^{2}+y^{4}\) into a product of polynomials of lower degree.
(b) Decide whether the number \(9^{1998}+3^{1998}+1\) is prime.
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Serbian Republic Competition (Republicko takmicenje) 1998, high school grade I, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source