Is it sufficient to offer salutations to a colleague at work with whom you've had a disagreement, or is it obligatory to shake his hand, especially since his colleague does not show interest in his salutation?

The boycotter's deeds are not raised, and every servant who does not associate partners with Allah is forgiven except for the boycotter. The best among those who boycott is the one who initiates the greeting of peace. It is not permissible to boycott for more than three days, and the most complete act is shaking hands, as the Prophet, peace and blessings be upon him, said: "It is not lawful for a Muslim to boycott his brother for more than three days, so that when they meet, this one turns away and that one turns away. The best of them is the one who initiates the greeting of peace." And according to his, peace and blessings be upon him, saying: "Indeed, when a believer meets another believer and greets him with peace and takes his hand and shakes it, their sins fall away just as the leaves of a tree fall." If you suffice with greeting and cheerfulness, there is no harm. Among the prophetic directives are: "Connect with him who cuts you off, give to him who deprives you, and forgive him who wrongs you," and similarly: "Shall I not tell you about the noblest morals of this world and the hereafter: that you forgive him who wrongs you, give to him who deprives you, and connect with him who cuts you off."