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(c) Prove that ifa,b,care odd integers anda+b+c= 0, thenabc <0.Problem 2.4 (Direct Proofs).(a) Prove that ifnis an odd integer, then2n2+ 4n-1is odd.(b) Prove that every odd integer is the difference of two perfect squares. (Hint: collect some data on small oddintegers to look for patterns.)(c) Prove that ifais any odd integer andbis any even integer, then2a+ 3bis even.(d) Prove that there exist 1000 consecutive positive integers that are not perfect squares.Solution 2.4.