Does there exist an infinite number of positive integer triplets (x,y,z) with x < y < z such that:
x, y and z describe an arithmetic sequence, and:
Each of xy+1, yz+1 and zx+1 is a perfect square?
Give reasons for your answer.
Clarice Lispector, renowned brazilian writer and poetress, with simple phrases wrote a little masterpiece. The phrases (a version into English) she used are shown below, but not in order. Once you realized the proper order youīll find out the beauty of what she wrote because, if you read it downwards, itīs the end of a love affair, and if you read it upwards, itīs a confession of a great passion. Can you just rearrange the phrases below to achieve this? You canīt add anything and the punctuations already made belong to the phrases where they are. All the initials I capitalized deliberately to make it not too easy, but in the original only those who start a phrase are capitalized.
I still want you, as I always did.
I`m sure that
I feel inside that
I already forgot you!
I`ll be lying if I say that
And Iīll never use again the phrase
Nothing was in vain.
Sorry, but I must tell you the truth:
You donīt mean anything to me.
I love you!
I couldnīt ever say that
Itīs too late...
I donīt love you anymore.
I preserve a great love.
I feel more and more that
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