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Iff

Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

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Relative Powers

Weekly Problem 10 - 2007
The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

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Summing Squares

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Square Sum

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

One of the following is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

A: 118, B: 128, C: 138, D:148, E:158

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.
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