



 
Hi Roger, If it was just $\gcd(a^2  b^{2}, a+b)$ it would be easy since $a^2  b^2 = (a+b)(ab)$ but I can't factor $a^2 + b^{2}.$ Whatever the value is of $\gcd(a^2  b^{2}, a+b)$ it must be true for any allowable values of $a$ and $b.$ I would try some examples. Choose two relatively prime integers $a$ and $b,$ evaluate $a^2 + b^2$ and $a + b$ and find their gcd. Try it again for another pair of relatively prime integers. and again. What did you learn? Penny 



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