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None. Saudi Arabia is the only country that borders Egypt to the east besides Israel. Jerusalem is too close to Cairo to be considered for this question, and is also north of Riyadh. Riyadh itself is 1000 miles southeast of Cairo, so it makes no sense that there would be a capital city equidistant from the two. Sudan Borders Egypt to the south, but its capital Khartoum is 1000 miles from Cairo. However, the capitals of Yemen and Oman, both south of riyadh (saudi arabia) are roughly 720 miles from riyadh. However, they do not meet the requirements for this question, as they are 1300 and 1700 miles from Cairo respectively.

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