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.
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?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
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.View the archive of all weekly problems grouped by curriculum topic