Question

Let A, B in ℤ. Knowledge of PPF(A) and PPF(B) simplifies many computations. Let A = p₁^a₁...pₘ^aₘ and B = p₁^b₁...pₘ^bₘ.

Answer 1

In each case (a), (b), and (c), it is not possible to conclude that A = B.

Step-by-step explanation:

(a) No, we cannot conclude that A = B if A × F = B × F. Consider the case where A = 2 and B = 4, and F = 2. A × F = 2 × 2 = 4, and B × F = 4 × 2 = 8, but A does not equal B. Therefore, we cannot make this conclusion.

(b) No, we cannot conclude that A = B if A FB F. This statement is unclear, but assuming it means that A is a factor of B and F, then we can consider the case where A = 2, B = 4, and F = 2. A is a factor of both B and F, but A does not equal B.

(c) No, we cannot conclude that A = B if FÃ = BF. Again, assuming that FÃ means F is a factor of A, consider the case where A = 4, B = 2, and F = 2. 2 is a factor of A, and 2 × 2 = 4, but A does not equal B.