Prove or disprove the statement. For all integers x, y and z, if x|y and x|z, then x|( ) (6𝑦2 − 𝑧2

Let x, y, z be integers. Decide if each of the following statements is true orfalse. If the statement is true, then prove it. If the statement is false, then give a counterexample(a) If x(y − z) = 0, then y = z.

f x, y and z are consecutive positive integers such that x < y < z, then which of the following must be true ?I. xyz is divisible by 6.II. (z – x) (y – x + 1 ) = 4III. xy is odd.

If x y and y z, which statement must be true?A.x zB.x zC.x zD.z x

If 𝑛 is a natural number, then 252n−92𝑛 is always divisible by

Prove that 𝒏(𝒏𝟐 + 𝟓) is divisible by 𝟑 for any integer 𝒏 ≥ 𝟎