Final answer:
The presented symptoms suggest the elderly man is suffering from pellagra, a type of malnutrition due to protein and niacin deficiency, commonly associated with a corn-based diet.
Step-by-step explanation:
The elderly man's symptoms of chronic diarrhea, pigmented regions on hands, arms, and face, mild dementia, and a smooth and shiny tongue indicate that he is suffering from malnutrition, specifically, a type of protein deficiency known as pellagra. Pellagra is caused by a deficiency of niacin (vitamin B3) and commonly presents with the three D's: dermatitis, diarrhea, and dementia. Given his limited diet of mostly corn, which lacks niacin and other vital nutrients, in conjunction with little fresh foods, this result in insufficient intake of essential proteins and calories. The smooth, shiny tongue is indicative of glossitis, which is commonly seen in nutritional deficiencies. Treatment would involve nutritional rehabilitation with a focus on a balanced diet rich in proteins and vitamins.