The topic will require an examination of two issues
Paul's teachings
Luther's teachings
First of all the teachings are unique in the sense that they address problems and set out to correct those problems.
Paul's Teaching
Paul faced a problem with his listeners, consisting of both Jewish and Gentile believers. Both were puzzled by what the inclusion of Gentiles in the group identified by the label People of God meant.
Were Gentiles included because they had become as righteous, or more righteous than the Jews? No, the change occurred because of no reason, it was a gift, not earned.
Were Gentiles to convert to Judaism? No, because while the promises of the Old Covenant required conversion to Judaism, those of the New Covenant required only faithfulness to Jesus.
These were the main issues the inclusion of Gentiles raised, and for our purposes we will study the second.
The Jewish believers found it hard to grasp that the Old Convenant had disappeared. God had ALWAYS required circumcision as a requirement for entry.
So Paul showed how Abraham entered friendship with God just by believing. Faith alone, without working, without circumcision. The approval was recorded to show that God's People were always identified as those with faith, and the minimum requirement had never been any exertion. Israel was a subset of God's People to whom Law had been added, and Gentiles never ever belonged to that subset. Rather than being a standard, Israel was the exception.
Paul's teaching, when understood, solved the problem of whether conversion to Judaism was required. Clearly, it was not. Gentiles became a part of God's People by believing, just like Abraham. Abraham was the precedent, the father, the prototype.
Luther's teaching
Luther faced a problem with the RCC. Their tradition taught men were saved by faith and effort. This effort was from the church and it was activated by payment! It was clear to Luther that this process was not in sync with Christianity on so many levels, and he tried to correct it by using Scripture.
His study showed him entry into the community of God's People was by faith, and no effort was required.
He saw Paul's attack on law as nullification, the text notwithstanding.
Roman's 3
31Do we then nullify the Law through faith? May it never be! On the contrary, we establish the Law.
Those who resorted to law keeping for approval were killed. The answer was to turn to the Gospel, which promised justification through faith alone.
I repeat.
Turning to law was death.
Turning to the Gospel was life.
And the Gospel was to believe on the Lord Jesus.
Unfortunately, in the Ancient Near East, faith was understood to mean loyalty, and not the meaning of cognitive belief it had come to be understood, in the centuries after, in the West.
So in the ANE, if a person became a follower of a leader, his condition was perfected, confirmed, PROVED, by loyal responses to SITUATIONS, reinforcing the initial approval.
James 2
21Was not Abraham our father justified by works when he offered up Isaac his son on the altar?
22You see that faith was working with his works, and as a result of the works, faith was perfected;
23and the Scripture was fulfilled which says, “AND ABRAHAM BELIEVED GOD, AND IT WAS RECKONED TO HIM AS RIGHTEOUSNESS,” and he was called the friend of God.
24You see that a man is justified by works and not by faith alone.
25In the same way, was not Rahab the harlot also justified by works when she received the messengers and sent them out by another way?
26For just as the body without
the spirit is dead, so also faith without works is dead.
So was the RCC right and Luther wrong?
Well the RCC taught that righteousness required for a good welcome into the Kingdom was imparted to the believer through Grace, administered through God's church, the, ahem, RCC.
And Luther?
His study of Scripture told him righteousness, sanctification, was IMPUTED.
However, that's beyond the scope of this discussion. More actors come into play, and more languages too.
Hint
Erasmus and Latin jump in.
Suffice to say that faith alone guarantees entry, and works prove the depth of that faith.