Prove that from the only Book of The Bible whose stated purpose for being written is to tell people how to have life (Eternal Life).
And truly Jesus did many other signs in the presence of His disciples, which are not written in this book; but these are written that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in His name.
You have to examine all scripture on a topic, not just the ones you like.
Belief and repentance are absolutely required to be saved - no repentance, and no salvation.
To start with, Jesus said HE CAME to call sinners unto repentance, and warned that unless we repent we PERISH:
Luke 5:30 And the Pharisees and their scribes grumbled at his disciples, saying, “Why do you eat and drink with tax collectors and sinners?”
Luk 5:31 And Jesus answered them, “Those who are well have no need of a physician, but those who are sick.
Luk 5:32
I have not come to call the righteous but sinners to repentance.”
Luk 13:3 No, I tell you;
but unless you repent, you will all likewise perish.
In addition to the fact that Jesus came to call sinners unto repentance, He also said after His resurrection that
repentance for the remission of sins must be preached to all nations:
Luk 24:46 And said unto them, Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day:
Luk 24:47
And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.
Repentance is absolutely required for salvation.
And as Jesus was about to ascend, He told the apostles in Matthew 28:19 to make disciples of all men,
teaching them all He commanded them, which would include the need to repent of sins.
Jesus also gives the example of a man at the altar repenting of his sins and being forgiven:
Luk 18:13 But the tax collector, standing far off, would not even lift up his eyes to heaven, but beat his breast, saying, ‘God, be merciful to me, a sinner!’
Luk 18:14 I tell you, this man went down to his house justified,
And other scriptures presented here, will further establish that repentance - which includes asking God to forgive our sins - is required for salvation, alongside faith.
John wrote that we must confess our sins, to have them forgiven:
1Jn 1:9 If we confess our sins, he is faithful and just to forgive us oursins, and to cleanse us from all unrighteousness.
Paul preached both faith AND repentance is necessary, not just faith:
Act 20:20 Andhow I kept back nothing that was profitable unto you,but have shewed you, and have taught you publickly, and from house to house,
Act 20:21 Testifying both to the Jews, and also to the Greeks, repentance toward God,
AND faith toward our Lord Jesus Christ.
Repentance towards God, and faith towards Jesus: both are needed, and are separate - repentance is not automatically part of faith.
And Paul further elaborates that repentance AND faith are required
Act 26:19 “Therefore, O King Agrippa, I was not disobedient to the heavenly vision,
Act 26:20 but declared first to those in Damascus, then in Jerusalem and throughout all the region of Judea, and ALSO to the Gentiles,
that they should repent AND turn to God, performing deeds in keeping with their repentance.
In one text, Paul preached repentance toward God AND faith towards Jesus - in another that we should repent AND turn to God.
Then in Acts 3:19, we are told to repent and be converted for the forgiveness of our sins:
Act 3:19 Repent therefore, and be converted, that your sins may be blotted out
In that text, repentance clearly precedes conversion and forgiveness of our sins - and as 1 John 1:9 makes plain, repentance includes confessing our sins to God, for their forgiveness.
Albert Barnes explains this about Acts 3:19:
“Sin cannot be pardoned before man repents of it. In the order of the work of grace,
repentance must always precede pardon. Of course, no man can have evidence that his sin is pardoned until he repents. Compare Isa 1:16-20; Joe 2:13”.
Repentance must always precede pardon.
And the account by Jesus of the unforgiving servant asking God to forgive his sins and the king then forgiving him, and 1 John 1:9, backs that up perfectly.
If it were true as some claim that repentance happens after conversion, or is part of it, then Acts 3:19 would say this: Be converted and repent, that your sins be forgiven - instead of saying to repent and be converted.
Peter also told those 3,000 who were added to the church that day, to repent, and be baptized, in Acts 2:38.
It is unequivocally clear that repentance is separate from faith; that repentance is needed, alongside faith, as part of being saved ; and that repentance includes asking God to forgive our sins, and not just changing our minds about sin. 
