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Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

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Iff

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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Triangles Within Squares

Can you find a rule which relates triangular numbers to square numbers?

Smith and Jones

Age 14 to 16 Challenge Level:

Have you listed the square and cube numbers between 13 and 1300?

Consider how many numbers satisfy each set of conditions:
Less than 500, square and cube
Less than 500, square and not cube
Less than 500, not square and cube?