applied math Prove that
(a) $5n^2 + 3n + 4$ is even , for all integers n.
(b) for all integers n, if $5n+ 1$ is even, then $2n^2 + 3n + 4$ is odd.
(c) the sum of five consecutive integers is always divisible by 5.
(d) $n^3 - n$ is divisible by 6, for all integers n.
(e) $(n^3 - n)(n + 2)$ is divisible by 12, for all integers n.
(f) every four-digit palindrome number is divisible by 11. (A palindrome
number is a number that reads the same forward and backward.)
(g) if a, b, and care real numbers and (a - bi)(c - ci) = 1 - i, then ac = l.
(h) if p is a prime integer, then p + 19 is composite.
(i) if n is a natural number and r is the remainder when n is divided by 3,
then if t = 5 or 11, the sum $r^2+ r + t$ is prime.
(j) if m and n are natural numbers , $n < 4$, and $(2 - n)(2 - m) > 2(m - n)$,
then m = 1 or n = 3.
(k) if $n > 2$ is an even natural number, then 2n - 1 is not prime.
(]) if S is a set of real number such that a, bare in S, and if $x\leq S$ a and $x\leq b$
for every element x of S, then a = b.
(m) if a and b be integers and b is odd, then 1 and -1 are not solutions of the
equation $ax^4 + bx^2 + a = 0.$
(n) if two nonvertical lines have slopes whose product is -1, then the lines
are perpendicular. 2nd EditionDaniel J. Velleman 12th EditionPatrick J. Hurley 12th EditionPatrick J. Hurley 11th EditionPatrick J. Hurley