54841=317×173.\large 54841 = 317 \times 173.54841=317×173.
54841, whose prime factor decomposition is given above, can be written as the sum of two perfect squares in two different ways:
54841=a2+b2=c2+d2,54841 = a^2 + b^2 = c^2 + d^2,54841=a2+b2=c2+d2,
where a,b,ca,b,ca,b,c and ddd are distinct positive integers. Find the sum a+b+c+da+b+c+da+b+c+d.
Hint: 317=196+121317 = 196 + 121317=196+121, and 173=169+4173 = 169 + 4173=169+4.