OK, this is my understanding of RSA-style encryption:

First, one picks two distinct primes, $p$ and $q$. The message is then encoded using a modulus $n = pq$.

The encryption key $e$ is then chosen to be an integer $1 < e < \varphi(n)$, where $\varphi$ is the Euler totient function.

The message $m$ (which is an integer) is then turned into the ciphertext $c = m^e\text{ (mod }n)$.

Together, $(e,n)$ make up the public key.

The private key (which must be kept secret) is $(d,n)$, where $d = e^{-1}\text{ (mod }\varphi(n))$

The message $c$ is sent to the holder of the private key.

To recover the plaintext $m$, one computes:

$c^d = (m^e)^d = m^{ed} = m^{ee^{-1}} = m\text{ (mod }\varphi(n))$

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I am unfamiliar with your notation, so what follows here is just a guess:

$p = 5, q = 41$, so that $n = 205$ and $\varphi(n) = \varphi(5)\varphi(41) = (4)(40) = 160$.

Presumably, we have "two messages" encoded, $c_1 = 1$ and $c_2 = 115$

Presumably the encryption key is $77$.

To find the decryption key, we compute $(77)^{-1}\text{ (mod }160)$, which we have previously found to be $133$.

Next, we calculate $1^{133}$ and $115^{133}$ modulo $205$.

The first one is easy, it will be $1$. The second one is a bit more involved. I do not know what this "method of repeated squaring" is, but it may be similar to what I have done below (and my calculations may be off).

Working mod 205, we have:

$(155)^{133} = (115)((155)^2)^{66}$. As $115^2 = 13225 = 13120 + 105 = 64*205 + 105$, this is:

$= (115)(105)^{66} = (115)((105)^2)^{33}$. Now $105^2 = 11025 = 10856 + 160 = 53*205 + 160$, so:

$= (115)(160)^{33} = (115)(160)(160)^{32}$. Dealing with the left first, we have $(115)(160) = 18400 = 18245 + 155 = 89*205 + 155$, so we have:

$= (155)(160)^{32} = (155)((160)^2)^{16}$. So (whew, this tires me out) $160^2 = 25600 = 25420 + 180 = 124*205 + 180$, and:

$= (155)(180)^{16} = (155)((180)^2)^8$. Same process: $180^2 = 32400 = 32390 + 10 = 158*205 + 10$, thus:

$= (155)(10)^8 = (155)(100)^4 = (155)(100^2)^2$. Here, $100^2 = 10000 = 9840 + 160 = 48*205 + 160$, and we get:

$ = (155)(160)^2 = (155)(180)$ (we calculated $160^2$ earlier). As $(155)(180) = 27900 = 27880 + 20 = 136*205 + 20$, we finally arrive at:

$= 20$.

So the decrypted numerical message is: <1,20>, that is the text message is: <A,T>.

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The above has a lot of guesswork on my part, and my calculations may be wrong.