Q: What is meant by the term conjecture?

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The Poincaré Conjecture.

One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.

My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.

One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.

There is no logical conjecture that can be made for what could be an irregular polygon with an unknown number of sides. Of course, you could always conjecture anything. For example, that they will taste of strawberries. A conjecture that, I guess, will be disproved quite easily.

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