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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.
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.
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?