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Odd Differences
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Triangular Triples
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Iff
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Age 14 to 16 Short
Challenge Level
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.