$T^2 - K^2= 41$ , $O = T\times K$ , what is the sum of all positive factors of $O$ ?

The answer is 1344.

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I am assuming that T and K are both positive integers. $T^2 - K^2= 41\Rightarrow(T+K)(T-K)=41$ . Since 41 is prime, and $T-K<T+K$ , we get $T-K=1$ , $T+K=41$ . Solving, we get $T=21$ , $K=20$ .

Thus, $O=420$ and the sum of factors is therefore 1344.