Square Battalions

A general formed his men into a square (that is, an equal number in rank and file) and he found that he had an excess of 59 men.  Then he increased both rank and file by one man equally and, forming a square, found that he was 84 men short.  How many men did he have at his command?

Soulé's Philosophic Practical Mathematics, George Soulé, 1905

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