# 1977 AHSME Problems/Problem 11

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## Problem 11

For each real number , let be the largest integer not exceeding (i.e., the integer such that ). Which of the following statements is (are) true?

## Solution

Solution by e_power_pi_times_i

Notice that is just . We see that is true, as adding by one does not change the fraction part of the number. Similarly, is false, because does not always equal (If both numbers were , , ). Because is true and is false, the answer is .