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Sum of Any Three Consecutive Integers | ||
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Observation I | Observation II | Observation III |
2+3+4=9=3⋅3
|
7+8+9=24=3⋅8
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13+14+15=42=3⋅14
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Conjecture: The sum of any three consecutive integers is three times the second number. |
However, it is unknown whether any given conjecture holds true for all cases. It could be false under some circumstances and, therefore, cannot be used to support other claims. A counterexample is enough to prove that a conjecture is false. When a conjecture is rigorously proved, it becomes a theorem.
One of the best-known conjectures is Goldbach's Conjecture, named after the German mathematician Christian Goldbach.
Goldbach's Conjecture |
Every even whole number greater than 2 is the sum of two prime numbers. |