918 A mathematical contest
4 Determine all pairs of nonnegative integers(m, n)which are solu-
tions to the equation3(2m)+1=n^2.5 Letf(n)=n^4 +2n^3 −n^2 +2n+1.(a) Show thatf(n)can be written as the product of two quadratic
polynomials with integer coefficients.(b) Determine all integersnfor which|f(n)|is a prime number.