Prove the theorem, due to Kraitchik, asserting that 13|2^70+3^70 Choose the correct answer.
A) 1^70+3^70 == 0 (mod 13), or 1|2^70+3^70 B) 2 C) 1 D) 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70 E) 1
By Fermat's theorem we have 2^12 == 1 (mod 13), hence 2^60 == 1 (mod 13), and since 2^5 == 6 (mod 13), which implies 2^10 == -3 (mod 13), we get 2^70 == -3 (mod 13). On the other hand, 3^3 == 1 (mod 13), hence 3^69 == 1 (mod 13) and 3^70 == 3 (mod 13). Therefore 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70, which was to be proved.   So Answer is 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70 2^70+3^70 == 0 (mod 13), or 13|2^70+3^70
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Prove the theorem, due to Kraitchik, asserting that 13|2^70+3^70