in Deuteronomy 24:1-4 a divorced woman can marry other man. And if the the new husband dies, the first husband cannot remmary his ex-wife, nothing about adultery in here.
But the Greek books state that Jesus disagrees with Moses and changed the permission in Deuteronmy 24 as quoted in Greek book Mark 10.
In short the Christians are saying Bible is not entirely words of God due to Deut 24 not a revelation from God.
Moses permitted men to divorce their wives and give them a certificate of divorce because of the hardness of their hearts. They had to have a reason to divorce and that was "ervah"which is uncleanness. This was abused as they would divorce their wives for any reason they saw fit and would claim this to be uncleanness. He permitted the divorce because many husbands would just send their wives away without a certificate to show they were divorced and these women would end up killed because they had no proof for their divorce and would be deemed "adulterous". So, although adultery is not mentioned, it is in their laws and that is why Moses permitted the divorce with a certificate. The husbands also did not want to give a certificate because they would have to give back any money, animals, etc. that the gained by marrying the wife.
When Jesus came and was tested, He reaffirmed what Moses said; He did not contradict Moses. Jesus said you could divorce and remarry in the case of "porneia" in Greek, which means uncleanness.
Remember, Jesus said "He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but
from the beginning it was not so." Jesus is discussing God’s will for marriage “from the beginning”. God's original marriage plan, as instituted in Eden, had ideally never changed, though a relaxation of it had been allowed under Moses. But here, Jesus preceded to restore marriage to its original intent.
The divorce mentioned in Deuteronomy 24:1-4 is not a command from God, but was permitted by Moses, as Jesus confirms (Matthew 19:8). Why did Moses permit divorce? Moses perceived that if divorce were not permitted, in many cases, the women would be exposed to great hardships through the cruelty of their husbands (hardness of their hearts). Moses tolerated a relaxation of the strictness of the marriage bond--not as approving of it, but to prevent still greater evils. And therefore if they had not been allowed to put away their wives, when they had conceived a dislike of them, they would have used them cruelly, would have beaten and abused them, and perhaps have murdered them. “But from the beginning it was not so” is repeated, in order to impress upon His audience the temporary character of this Mosaic relaxation. Moses did not direct it, or suffer it, in any such sense as to imply that God approved of it, or that it was right. It was a temporary regulation, suffered for a time on account of the wickedness of men, and in order to prevent the greater evils which that wickedness would otherwise have occasioned. It was a regulation as to the mode of putting away; not to justify that wrong practice, but to lessen, in some measure, its evils.
So Deuteronomy 24:1-4 does not contradict Jesus' teaching on marriage and divorce and Jesus' is teaching what God implemented in the beginning when there was not hardness of hearts from wicked men.
Also, God Himself demonstrated Jesus' teaching by divorcing Israel and giving her a bill of divorcement for the reason of adultery.