In the six rows of numbers below, each of the pairs adds up to 25. Now
25 happens to be a perfect square.
Fill in the blanks with a third number (a different number in each row)
so that the sums of any two numbers on any row is a perfect square.
++++
 1 24  
++++
 2 23  
++++
 3 22  
++++
 4 21  
++++
 5 20  
++++
 6 19  
++++
(In reply to
The algebra by Jer)
It's not all Pythagorean triple, just the ones like (5,12,13) and (7,40,41)...(2a+1, 2a²+2a, 2a²+2a+1)
For pairs that add to (2a+1)², call them n and (2a+1)²n
you can add the quantity n²+n(4a²4a1)+(4a^4+8a³+4a²)
which yields the squares
n²+n(4a²4a)+(4a^4+8a³+4a²) = (n(2a²+2a))²
and
n²+n(4a²4a2)+(4a^4+8a³+8a²+4a+1) = (n(2a²+2a+1))²

Posted by Jer
on 20130610 15:28:26 