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Simple Arithmetic

Incredibly, the great number theorist Ernst Kummer was so inept at simple arithmetic that he often asked students to help him in class. On one occasion, Kummer sought the result of a simple multiplication. "Seven times nine," he began. "Seven times nine is er -- ah -- ah -- seven times nine is..." "Sixty-one," a mischievous student suggested and Kummer wrote the "answer" on the blackboard. "Sir," another one interjected, "it should be sixty-nine." "Come, come, gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other!"

[According to Paul Erdos, Kummer calculated the result using the following logic: "The product cannot be 61, because 61 is a prime number; it cannot be 65, because 65 is a multiple of 5; 67 is a prime; and 69 is too big. Only 63 is left."]

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