Is a purchase valid if an agent is instructed to buy a slave for a hundred and buys one without a price, where the slave is worth exactly one hundred?

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The purchase is valid if the agent is instructed to buy a slave for one hundred and purchases a slave who is indeed worth one hundred without explicitly stating the price. This is permissible because if the purchase at one hundred would have been valid, purchasing it for less is considered an improvement, making the transaction permissible.