Problem

Suppose a, b, c, and d are integers. Prove that (a) 2a − 1 is odd. (b) if a is...

Suppose a, b, c, and d are integers. Prove that

(a) 2a − 1 is odd.

(b) if a is even, then a + 2 is odd.

(c) if a is odd, then a + 2 is odd.

(d) a(a + 1) is even.

(e) 1 divides a.

(f) a divides a.

(g) if a and b are positive and a divides b, then a b.

(h) if a divides b, then a divides bc.

(i) if a and b are positive and ab = 1, then a = b = 1.

(j) if a and b are positive, a divides b and b divides a, then a = b .

(k) if a divides b and c divides d, then ac divides bd.

(l) if ab divides c, then a divides c.

(m) if ac divides bc, then a divides b.

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Solutions For Problems in Chapter 1.4