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The problem Shifting Times Tables offers an introductory challenge for exploring linear sequences.
The problem Remainders explores some properties of numbers which could be useful when thinking about this problem.Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?