[update] Understanding why for n=1;n+2 ((n^2)-1)%8==0 isn't the point of this exercise...look at the pattern in the results of each iteration. That's what has me baffled. Haacked has a great proof explaining what's going on on the left side of the operand, but I'm more interested in what's up with the right side. [/update]

This just popped into my head the other day for no other reason than to bug me:  Square all odd numbers starting with 1…subtract 1 from the result…then divide by 8.  Now look for the pattern in the results.

 
for (int i = 1; i < 100; i += 2)
 {
    int iSquared = (i * i); 
    if (((iSquared) - 1) % 8 == 0)
    {
        int result = ((iSquared - 1) / 8);
        Console.WriteLine(i + "^2 = " + iSquared + " - 1 = " + ((iSquared) - 1) + " / 8 = " + result);
    }
    else
    {
        Console.WriteLine("false"); 
    }
}
Console.ReadLine(); 

Squint for a second or 2 and you’ll see it.  Anyone out there with a degree in mathematics care to explain why that happens?

Share this post: | | | | |