Prove that
(a) for all integers n, 5n2 + 3n + 4 is even.
(b) for all odd integers n, 2n2 + 3n + 4 is odd.
(c) the sum of 5 consecutive integers is always divisible by 5.
(d) if two nonvertical lines have slopes whose product is then the lines are perpendicular.
(e) for all integers n, n3 – n is divisible by 6.
(f) for all integers n, (n3 − n)(n + 2) is divisible by
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