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Square of an Odd (Posted on 2002-10-06) Difficulty: 2 of 5
Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.

See The Solution Submitted by martyn    
Rating: 3.1333 (15 votes)

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Solution Puzzle solution ( Continued) | Comment 18 of 20 |
(In reply to Puzzle solution by K Sengupta)

SOLUTION TO PART B:

When n = p(p+1)/2, then n is called a Triangular Number.


Putting p = 1,2,3,.... in turn, the first few triangular numbers (excluding zero) are :
1, 3, 6, 10, 15, 21, .....

Since, the Triangular numbers are of the form p(p+1)/2, the ith Triangular Number will always be equal to the sum of the first i natural numbers.

Accordingly:
1 = 1
3 = 1+2
6 = 1+2+3
10 = 1+2+3+4
15 = 1+2+3+4+5


  Posted by K Sengupta on 2007-04-20 12:23:11
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