Encrypting plaintext with RSA encryption scheme

Question

I have an RSA encryption scheme with parameters

$p$ = 31
$q$ = 37
$e$ = 17

I've decrypted the ciphertext $y$ = 2, using CRT and got the following plaintext: $8440 = 721 \pmod{1147}$

Now I would like to verify this answer by encrypting the plaintext without using the CRT, but I am not sure how to proceed with this.

Update: After doing a bit of research, I've found the RSA Encryption function:

Given the public key (n,e) = kpub and the plaintext x, the encryption function is:

$y = e_\text{kpub}(x) = x^e \pmod n$

So is the following correct?

$y = 721^{17} \pmod{1147}$

Answer 1

Following the equation for RSA Encryption:

$y = e_{kpub}(x) = x^e$ $ mod $ $ n$

We can encrypt our plaintext, x = 721, by the following:

$e = 17$ $n = 1147 (n = p*q = 31*37)$

$y = 721^{17} $ $ mod$ $ 1147$

Which reduces to:

$y = 2$