Homework SourseDetermine whether the statement is true or false Prove the s
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.
Solution
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
