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.
(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
Puzzle solution ( Continued)
