Let p and p+2 be twin primes. Prove that Euler phi-function(p+2)= Euler phi-function(p) +2.
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$\displaystyle \phi(p) = p-1 $ and $\displaystyle \phi(p+2) = (p+2)-1 = p+1 $ since both $\displaystyle p $ and $\displaystyle p+2 $ are prime. so $\displaystyle \phi(p+2) = p+1 = (p-1)+2 = \phi(p)+2 $.
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