1) Given the sequence: 2 ; 5 ; 8 ; ...
a) Prove that none of the terms of this sequence are perfect squares.
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This sequence is an arithmetic progression with the common difference of 3 and the first term 2. When dividing by 3, all the terms of the progression give the remainder of 2. No one perfect square gives the remainder 2 when is dividing by 3. Proved.
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