Determine whether the statement is true or false. Prove the statement directly f

Question

Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counter example if it is false. For all integers a and b, if a|b then a^2|b^2. Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counter example if it is false. For all integers a and b, if a|b then a^2|b^2. Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counter example if it is false. For all integers a and b, if a|b then a^2|b^2.

Explanation / Answer

if a|b, then there exists an integer c such that

b = ac

=>

b^2 = a^2*(c^2)

=>

a^2 | b^2

thus proved

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