Prove the following statements. a. Let a € Z, then 3|(2a² + 1) if and only if 3 a. b. Let a € Z. If 2|(a² – 5) then 4|(a²-5). (Hint: For justification you might want to use Q5b). c. Let a € Z. If 2(a² − 1) then 8|(a² − 1). d. If a is an integer and a²la then a € {−1,0, 1}. e. Let a, b, c € Z if a² + b² = c² then 3|ab.

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