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October 31st, 2018, 01:22 AM  #1 
Member Joined: Aug 2015 From: Chiddingfold, Surrey Posts: 57 Thanks: 3 Math Focus: Number theory, Applied maths  Mod functions related to Fermat's Last Theorem
Since Fermat's Last Theorem has been proved, can it be concluded that there can't be three different, relatively prime, non zero integers A>B>C where the following six Mod functions are all equal to zero when the power is odd and higher than one and all but the first Mod function are equal to zero when the power is even and greater than two? 1. A^n Mod (B + C) 2. B^n Mod (A  C) 3. C^n Mod (A  B) 4. (B^n + C^n) Mod A 5. (A^n  B^n) Mod B 6. (A^n  C^n) Mod C Answer believe it or not is NO. There are such sets of three integers. Before I reveal what they are, see if you can find them. Last edited by skipjack; October 31st, 2018 at 06:41 AM. 

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