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perfect squares

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U(n+1) = 2Un + 1 2011-05-22
From Cillian:
In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence
Answered by Claude Tardif.
Two problems 2010-04-13
From Dorothy:
1. Explain why the number 123, 456, 789, 101, 112 cannot be a perfect square. (Hint: What is the units digit?)

2. A substance doubles in volume every minute. At 9:00A.M., a small amount is placed in a container. At 10:00A.M., the container is just full. At what time was the container one-eighth full?

Answered by Robert Dawson.



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