341Is this a query or a challenge
In case its a query:
Fermat's theorem on primes 7 and 13
Show that a12-b12 is divisible by 91 if a and b are both prime to 91
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5 Answers
341341From Fermat's Theorem applied on a we have
a^6 \equiv 1 \pmod 7 \Rightarrow a^{12} \equiv 1 \pmod 7
Likewise b^{12} \equiv 1 \pmod 7 so that a^{12} - b^{12} \equiv 0 \pmod 7
Similarly a^{12} - b^{12} \equiv 0 \pmod {13}
Since gcd (7,13) = 0 this implies a^{12} - b^{12} \equiv 0 \pmod {91}