169 is a square and it is a sum of squares (169=122+52169 = 12^2 + 5^2169=122+52).
But its square can also be written as the sum of two squares. Let
1692=a2+b2\large 169^2 = a^2 + b^21692=a2+b2
with a>b>0a > b > 0a>b>0 and gcd(a,b)=1\gcd(a,b)=1gcd(a,b)=1.
Without using a calculator, find a+ba + ba+b.