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I don't see how there could be multiple solutions (a,b,p) for different alpha's. 1/a+1/b is unique and p/(p1^alpha1*p2^alpha2) is also unique.
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Project Euler #157: Solving the diophantine equation 1/a +1/b = p/10^n
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I don't see how there could be multiple solutions (a,b,p) for different alpha's. 1/a+1/b is unique and p/(p1^alpha1*p2^alpha2) is also unique.