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Triangular Square Numbers Triangular Square Numbers Aim The aim of this investigation is to investigate numbers that are both square and triangular. Part of this investigation will be to try to find a formula to calculate the nth triangular square number. Initial Analysis Triangular numbers are numbers calculated using the equation: Triangular square numbers must satisfy the above equation, and must also be square, so: Obtaining Data To investigate these numbers, some examples must be discovered. Finding these numbers by hand was tried, but it was found that triangular square numbers do not occur frequently in the set of natural numbers. A computer program was written and ran to find these numbers quicker, and therefore be more efficient. This program is shown in Appendix A, and the output file in Appendix B. This program finds all the triangular square numbers between 1 and 1 x 1016 - 1. It puts every number starting with 1 into the...

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