Number Theory - Euler's Theorem: 51 | 10^(32n+9) - 7

Jamers328

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Sep 20, 2007
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Use Euler's Theorem to confirm that, for any integer n >= 0,

51 | 10^(32n+9) - 7


Euler's Theorem: If n>= 1 and gcd (a,n) = 1, then a^(phi(n)) = 1 (mod n).
 
Start by computing ϕ(51)\displaystyle \phi(51). Then use Euler's Theorem to show a remainder of 1 when the exponent is 32n\displaystyle 32n. Then finish it.
 
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