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Let n be a positive integer. If \(a\equiv (3^{2n}+4)^{-1}\pmod{9}\), what is the remainder when a is divided by 9?

 Jan 6, 2019
edited by MathCuber  Jan 6, 2019

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The modular multiplicative inverse of an integer "a" modulo "m" is an integer "b" such that:
ab ≡ 1 mod m
If n = 1, a = 13^(-1)
If n = 2, a = 85^(-1).........and so on.
As a consequence of the above, no matter what the value of n, the multiplicative inverse of "a" will always be a 7. And as a result, 7a ≡ 1 mod 9.

 Jan 6, 2019
 #1
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+1
Best Answer

The modular multiplicative inverse of an integer "a" modulo "m" is an integer "b" such that:
ab ≡ 1 mod m
If n = 1, a = 13^(-1)
If n = 2, a = 85^(-1).........and so on.
As a consequence of the above, no matter what the value of n, the multiplicative inverse of "a" will always be a 7. And as a result, 7a ≡ 1 mod 9.

Guest Jan 6, 2019

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