Sophie Germain's theorem - Wikipedia, the free encyclopedia - 0 views
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Sophie Germain's theorem
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In number theory, Sophie Germain's theorem is a statement about the divisibility of solutions to the equation xp + yp = zp of Fermat's Last Theorem. Specifically, Sophie Germain proved that the product xyz must be divisible by p2 if an auxiliary prime θ can be found such that two conditions are satisfied: No two pth powers differ by one modulo θ; and p is itself not a pth power.