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Basically Silver Nitrate is not soluble in concentrated Nitric acid and therefore, there is no reaction between two. For example, if you take 1000 grams of concentrated HNO3 (~70%) then it will only dissolve 2 grams AgNO3. However, Silver Nitrate is slightly soluble in dilute Nitric acid. For example, 1000 grams 2HNO3, 3H20 only dissolves about 33.3 grams AgNO3. The temperature for this reaction is about 20°C (68°F). As a result of this reaction Silver Nitrate-Nitric Acid reagent is produced. Moreover, crystals are formed. This Silver Nitrate-Nitric Acid reagent that is formed from the reaction is used for the identification of sulfate.
To dissolve Siver Nitrate water is needed. So if you have a dilute solution of the acid, Silver Nitrate will dissolve somewhat because of the presence of water. However it will not dissolve in a concentrated Nitric Acid solution.