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

[Jamers328]

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).

 

[royhaas]

Start by computing \(\displaystyle \phi(51)\). Then use Euler's Theorem to show a remainder of 1 when the exponent is \(\displaystyle 32n\). Then finish it.